Search for η mesic 3He with the WASA-at-COSY facility in the pd -> 3He2γ and pd -> 3He6γ reaction

(1)

Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Search

for

η

mesic

3 He

with

the

WASA-at-COSY

facility

in

the

pd

→

3 He2

γ

and

pd

→

3 He6

γ

reactions

P. Adlarson

a

,

W. Augustyniak

b

,

W. Bardan

c

,

M. Bashkanov

d

,

S.D. Bass

c

,

e

,

M. Berłowski

f

,

A. Bondar

g

,

h

,

M. Büscher

i

,

j

,

H. Calén

a

,

I. Ciepał

k

,

H. Clement

l

,

m

,

E. Czerwi ´nski

c

,

R. Engels

n

,

A. Erven

o

,

W. Erven

o

,

W. Eyrich

p

,

P. Fedorets

n

,

q

,

K. Föhl

r

,

K. Fransson

a

,

F. Goldenbaum

n

,

A. Goswami

n

,

s

,

K. Grigoryev

n

,

t

,

L. Heijkenskjöld

a

,

1

,

V. Hejny

n

,

S. Hirenzaki

u

,

L. Jarczyk

c

,

T. Johansson

a

,

B. Kamys

c

,

N.G. Kelkar

v

,

G. Kemmerling

o

,

2

,

A. Khreptak

c

,

D.A. Kirillov

w

,

S. Kistryn

c

,

H. Kleines

o

,

2

,

B. Kłos

x

,

W. Krzemie ´n

y

,

P. Kulessa

k

,

A. Kup´s ´c

a

,

f

,

K. Lalwani

z

,

D. Lersch

n

,

3

,

B. Lorentz

n

,

A. Magiera

c

,

R. Maier

n

,

aa

,

P. Marciniewski

a

,

B. Maria ´nski

b

,

H.-P. Morsch

b

,

P. Moskal

c

,

H. Ohm

n

,

W. Parol

k

,

E. Perez del Rio

l

,

m

,

4

,

N.M. Piskunov

w

,

D. Prasuhn

n

,

D. Pszczel

a

,

f

,

K. Pysz

k

,

J. Ritman

n

,

aa

,

ab

,

A. Roy

s

,

O. Rundel

c

,

S. Sawant

ac

,

S. Schadmand

n

,

I. Schätti–Ozerianska

c

,

T. Sefzick

n

,

V. Serdyuk

n

,

B. Shwartz

g

,

h

,

T. Skorodko

l

,

m

,

ad

,

M. Skurzok

c

,

∗

,

4

,

J. Smyrski

c

,

V. Sopov

q

,

R. Stassen

n

,

J. Stepaniak

f

,

E. Stephan

x

,

G. Sterzenbach

n

,

H. Stockhorst

n

,

H. Ströher

n

,

aa

,

A. Szczurek

k

,

A. Trzci ´nski

b

,

5

,

M. Wolke

a

,

A. Wro ´nska

c

,

P. Wüstner

o

,

A. Yamamoto

ae

,

J. Zabierowski

af

,

M.J. Zieli ´nski

c

,

J. Złoma ´nczuk

a

,

P. ˙Zupra ´nski

b

,

M. ˙Zurek

n

,

6

a_Division_of_Nuclear_Physics,_Department_of_Physics_and_Astronomy,_Uppsala_University,_Box_516,₇₅₁₂₀_Uppsala,_Sweden b_Department_of_Nuclear_Physics,_National_Centre_for_Nuclear_Research,_ul._Pasteura_7,_02-093,_Warsaw,_Poland c_Institute_of_Physics,_Jagiellonian_University,_prof._Stanisława_{Łojasiewicza}_11,_30-348_Kraków,_Poland

d_School_of_Physics_and_Astronomy,_University_of_Edinburgh,_James_Clerk_Maxwell_Building,_Peter_Guthrie_Tait_Road,_Edinburgh_EH9_3FD,_United_Kingdom_of_Great BritainandNorthernIreland

e_Kitzbühel_Centre_for_Physics,_Kitzbühel,_Austria

f_High_Energy_Physics_Department,_National_Centre_for_Nuclear_Research,_ul._Pasteura_7,_02-093,_Warsaw,_Poland g_Budker_Institute_of_Nuclear_Physics_of_SB_RAS,₁₁_akademika_Lavrentieva_prospect,_Novosibirsk,_630090,_Russia h_Novosibirsk_State_University,₂_Pirogova_Str.,_Novosibirsk,_630090,_Russia

i_Peter_Grünberg_Institut,_PGI–6_{Elektronische}_{Eigenschaften,}_{Forschungszentrum}_Jülich,₅₂₄₂₅_Jülich,_Germany

j_Institut_für_{Laser– und}_{Plasmaphysik,}_{Heinrich–Heine}_Universität_Düsseldorf,_{Universitätsstr.}_1,₄₀₂₂₅_Düsseldorf,_Germany k_The_Henryk_{Niewodnicza´}_nski_Institute_of_Nuclear_Physics,_Polish_Academy_of_Sciences,₁₅₂_{Radzikowskiego}_St,_31-342_Kraków,_Poland l_{Physikalisches}_Institut,_{Eberhard–Karls–Universität}_Tübingen,_Auf_der_Morgenstelle_14,₇₂₀₇₆_Tübingen,_Germany

m_Kepler_Center_für_{Astro– und}_{Teilchenphysik,}_{Physikalisches}_Institut_der_Universität_Tübingen,_Auf_der_Morgenstelle_14,₇₂₀₇₆_Tübingen,_Germany n_Institut_für_Kernphysik,_{Forschungszentrum}_Jülich,₅₂₄₂₅_Jülich,_Germany

o_{Zentralinstitut}_für_Engineering,_Elektronik_und_Analytik,_{Forschungszentrum}_Jülich,₅₂₄₂₅_Jülich,_Germany

p_{Physikalisches}_Institut,_{Friedrich–Alexander–Universität}_{Erlangen–Nürnberg,}_{Erwin–Rommel-Str.}_1,₉₁₀₅₈_Erlangen,_Germany

q_Institute_for_Theoretical_and_Experimental_Physics_named_by_A.I._Alikhanov_of_National_Research_Centre_“Kurchatov_{Institute”,}₂₅_Bolshaya_{Cheremushkinskaya,} Moscow,117218,Russia

r_II._{Physikalisches}_Institut,_{Justus–Liebig–Universität}_Gießen,_{Heinrich–Buff–Ring}_16,₃₅₃₉₂_Giessen,_Germany

s_Department_of_Physics,_Indian_Institute_of_Technology_Indore,_Khandwa_Road,_Simrol,_{Indore 453552,}_Madhya_Pradesh,_India

t_High_Energy_Physics_Division,_Petersburg_Nuclear_Physics_Institute_named_by_B.P._Konstantinov_of_National_Research_Centre_“Kurchatov_{Institute”,}₁_mkr._Orlova roshcha,LeningradskayaOblast,Gatchina,188300,Russia

u_Department_of_Physics,_Nara_Women’s_University,_Nara_630-8506,_Japan

*

Correspondingauthor.

E-mailaddress:magdalena.skurzok@uj.edu.pl(M. Skurzok).

1 _Present_address:_Institut_für_Kernphysik,_Johannes_{Gutenberg–Universität}_Mainz,_{Johann–Joachim–Becher}_{Weg 45,}₅₅₁₂₈_Mainz,_Germany. 2 _Present_address:_Jülich_Centre_for_Neutron_Science_JCNS,_{Forschungszentrum}_Jülich,₅₂₄₂₅_Jülich,_Germany.

3 _Present_address:_Department_of_Physics,_Florida_State_University,₇₇_Chieftan_Way,_Tallahassee,_FL_32306-4350,_USA. 4 _Present_address:_INFN,_Laboratori_Nazionali_di_Frascati,_Via_E._Fermi,_40,₀₀₀₄₄_Frascati_(Roma),_Italy.

5 _Deceased.

6 _Present_address:_Lawrence_Berkeley_National_Laboratory,_Berkeley,_California_94720. https://doi.org/10.1016/j.physletb.2020.135205

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Articlehistory:

Received25September2019

Receivedinrevisedform7January2020 Accepted7January2020

Availableonline9January2020 Editor: L.Rolandi

Keywords:

η-mesicnuclei

ηmeson

We reportontheexperimentalsearchfortheboundstateofan

η

mesonand3_{He nucleus}_performed

using the WASA-at-COSY detector setup. In order to search for the

η

-mesic nucleus decay, the

pd→3_He2

_γ

_and_pd_→3_He6

_γ

_channels_have_been_analysed._These_reactions_manifest_the_direct_decay_of

the

η

mesonboundina3_{He nucleus. This}_non-mesonic_decay_channel_has_been_considered_for_the_ﬁrst

time. Whentakingintoaccountonlystatisticalerrors,theobtainedexcitationfunctionsrevealaslight indicationforapossibleboundstatesignalcorrespondingtoa3_He-

_η

_nucleus_width_above₂₀_MeV_and

bindingenergyBs between0and15MeV.However,thedeterminedcrosssectionsareconsistentwith

zero inthe rangeofthesystematicuncertainty. Therefore, asﬁnal resultweestimateonlythe upper limitforthecrosssectionofthe

η

-mesic3_{He nucleus}_formation_followed_by_the

_η

_meson_decay_which

variesbetween2 nband15 nbdependingonpossibleboundstateparameters.

1. Introduction

Strong attractive interactions between the ηmeson and nucle-ons mean that there is a chance to form η meson bound states in nuclei [1]. If discovered in experiments, these mesic nuclei would be a new state of matter bound just by the strong interaction with-out electromagnetic Coulomb effects playing a role. Strong interac-tion bound states are formed in a different way as compared to exotic atoms which involve binding of electrically charged mesons with nuclei. For the latter, negatively charged pions or kaons could replace an electron in an outer orbital in a standard atom and get bound in the atom due to the Coulomb interaction. The charged meson in such an excited state quickly undergoes transitions to the lower states until it is close enough to the nucleus and is either absorbed by the nucleus or lost in a nuclear reaction. For strong interactions, in contrast to the pion, the neutral ηmeson is special due to the strong attractive nature of this meson-nucleon interaction [1]. An off-shell ηmeson produced in nuclear reactions such as the pd

→

3He2

γ

and pd

→

3He6

γ

below the ηproduction threshold may form a bound state with the nucleus within which it is produced. Thus the absence of the electromagnetic interac-tion and the attractive nature of the η-nucleon interacinterac-tion, makes the case of the neutral η meson different from that of the pion or the kaon and opens the possibility for an exotic nucleus made up of the meson and nucleons. Early experiments with low statistics using photon [2,3], pion [4], proton [5] or deuteron [6–9] beams gave hints for possible η mesic bound states but no clear signal [10,11].

Here we present a new high statistics search for 3_He-

_η

_bound

states with data from the WASA-at-COSY experiment. We focus on the two main neutral decay channels of the η meson: η

→

2

γ

with branching ratio 39.41

±

0.20% and η

→

3

π

0

_→

₆

_γ

_with

branching ratio 31.54

±

0.22% [12]. These processes constitute more than 70% of the ηdecays. The choice of neutral decay chan-nels minimizes ﬁnal state interactions involving charged particles. Concurrent measurement of the two channels increases the

statis-tics and enables one to control systematic uncertainties in photons detection. The two-photon decay was previously suggested in [13] as a clean probe of the ηin nuclear media.

Considering the η-nucleus interaction, bound states can be formed by the attractive interaction with finite level width cor-responding to the finite lifetime of the state due to the absorptive interaction with the nucleus. The momentum distribution of the bound ηmeson determines the sum of the momenta of the emit-ted photons. Nuclear absorption and the additional ηdecay (disap-pearance) processes, reduces significantly the in-medium branch-ing ratio of 2

γ

and 6

γ

decay channels [14].

η

meson interactions with nucleons and nuclei are a topic of great experimental and theoretical interest. For recent reviews see [10,11,15–17]. Possible η-nucleus binding energies are related to the η-nucleon optical potential and to the value of η-nucleon scattering length aηN [18]. Phenomenological estimates for the

real part of aηN are typically between 0.2 and 1 fm depending

on the model assumptions. η bound states in helium require a large η-nucleon scattering length with real part greater than about 0.7–1.1 fm [19–21]. Recent calculations in the framework of optical potential [22], multi-body calculations [20], and pionless effective ﬁeld theory [19] suggest a possible 3_He-

_η

_{bound state.}

Modifications of meson properties are expected in medium. In studies of the transparency of nuclei to propagating mesons pro-duced in photoproduction experiments one finds strong η absorp-tion in nuclei [24]. For the η one finds weaker interaction with the nucleus. An effective mass shift for the ηin medium has been observed by the CBELSA/TAPS Collaboration [25]. The η-nucleus optical potential Vopt

=

Vreal

+

iW deduced

from these

photopro-duction experiments with a carbon target is Vreal

(

ρ

0

)

=

m∗

−

m

=

−

37

±

10

±

10 MeV and W

(

ρ

0

)

= −

10

±

2.5 MeV at nuclear

mat-ter density ρ0. This mass shift is very close to the prediction of the

Quark Meson Coupling mode (QMC) with mixing angle -20 degrees [13,26], which also predicts a potential depth about -100 MeV for the η at ρ0. The η results are also consistent with scattering

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Fig. 1. 2-D histogramsofenergiesdepositedinthefirstlayerofForwardTriggerHodoscope(FTH1)andthefirstlayerofForwardRangeHodoscope(FRH1)foralleventswith signalinForwardProportionalChamber(FPC)(leftpanel)andeventsthatwereidentifiedas3_{He (right}_panel).

search for η- nucleus bound states has also been performed with results reported in Ref. [29].

Hints for possible ηhelium bound states are inferred from the observation of strong interaction in the ηhelium system. One ﬁnds a sharp rise in the cross section at threshold for η production in both photoproduction from 3_{He [}₂_,₃₀_{] and in the proton-deuteron}

reaction dp

→

3He

η

[31]. These observations may hint at a re-duced ηeffective mass in the nuclear medium.

Previous bound state searches at COSY have been focused on the reaction dd

→

3_HeN

_π

_[₈_,₉_]._Studies_of_the_excitation

func-tion around the threshold for dd

→

4_He

_η

_did_not_reveal_a

struc-ture that could be interpreted as a narrow mesic nucleus. Up-per limits for the total cross sections for bound state production and decay in the processes dd

→ (

4He-

η

)

bound

→

3Hen

π

0 and

dd

→ (

4_He-

_η

₎

bound

→

3Hep

π

− were deduced to be about 5 nb

and 10 nb for the n

π

0 _and_p

_π

− _channels_respectively_[₉_]._The

bound state production cross sections for pd

→ (

3_He-

_η

₎

bound [32]

are expected to be more than 20 times larger than for dd

→

(

4He-

η

)

bound [33].

In May 2014 the experiment searching for ηmesic 3_He_nuclei

was performed at the COSY accelerator [34,35] in Jülich, Germany. The measurements were carried out using the WASA-at-COSY de-tector [36–40]. The mesic nuclei are supposed to be formed in proton-deuteron collisions. A ramped proton beam with beam mo-mentum varying in the range from 1.426 to 1.635 GeV/c cor-responding to 3_He

_η

_excess_energy_range_from

₋

_{70 to}_{30 MeV}

and a pellet deuterium target [41] were used. The 3_He-

_η

_bound

state was searched for in the pd

→ (

3_He-

_η

₎

bound

→

3He2

γ

and

pd

→ (

3_He-

_η

₎

bound

→

3He6

γ

decay channels. These channels that

manifest the direct decay of η bound in 3_He_nucleus_have_been

investigated for the ﬁrst time. The existence of the bound 3_He-

_η

state would manifest itself as a maximum or interference pattern in the excitation function for both of the studied reactions below the pd

→

3He

η

reaction threshold.

For the normalization of the excitation functions, the integrated luminosity was determined as a function of the excess energy. The analysis is presented in the next section. Further on, the data se-lection and eﬃciency determination is described. The data analysis is followed by the interpretation of the achieved excitation func-tions in view of the possible signal from the η-mesic 3_He.

2. Luminositydetermination

Luminosity was determined based on the pd

→

3_He

_η

_and

pd

→

ppnspectator reactions. The pd

→

3He

η

reaction analysis

al-lows one to estimate the integrated luminosity for 3_He

_η

_excess

energy Q3_He_{η above} zero. The 3He particles were registered in

the forward detector [36] and identiﬁed using the E

−

E method based on energy losses in scintillator layers (see Fig.1).

Fig. 2.3Hemissing massspectrumobtainedfromdatafortheexcess en-ergyrangeof Q3Heη ∈ [20.0; 22.5]MeV.Thepartofthespectrumthat

isconsideredtobebackgroundisshownwithgreencolour andisﬁtted withapolynomialoffourthpower(orange).

The count of events originating from this reaction was obtained based on the 3_{He missing mass spectra for each excess energy}

in-terval separately. An example spectrum is shown in Fig. 2. The reconstruction eﬃciency was calculated using Monte Carlo simu-lations taking into account the experimental data on cross sections and angular distributions [40,42–44].

The pd

→

ppnspectator reaction analysis allows one to

deter-mine the integrated luminosity for the whole beam momentum range. As far as the target overlapping by the beam is chang-ing during the acceleration cycle, the integrated luminosity value can change depending on the beam momentum. The registration eﬃciency for the pd

→

ppnspectator reaction was obtained with

dedicated Monte Carlo simulations described in Refs. [45,46]. The distribution of relative proton-neutron motion inside the target deuteron was calculated based on the parametrisation of the Paris potential [47]. Data on the proton-proton elastic scattering cross section and the angular distribution [48] were used for simulat-ing the quasi-elastic scattering in the framework of the spectator model. The calculated cross section was multiplied by the factor 0.96 to take into account the shading effect [49]. It is worth not-ing that above the η production threshold, the two estimates of luminosity are in agreement (based on the pd

→

ppnspectator and

pd

→

3_He

_η

_{reactions [}₄₅_{]). The total integrated luminosity was}

de-termined to be 2446

±

3(stat

.)

±

66(syst

.)

±

4(norm.) nb−1 where the statistical, systematic and normalisation errors are indicated, respectively [45]. This is the largest statistics ever obtained for these experimental conditions.

3. Theanalysisofpd

→ (

3_He-

_η

₎

bound

→

3He2

γ

and

pd

→ (

3He-

η

)

bound

→

3He6

γ

reactions

As a ﬁrst step, in order to establish the optimal selection crite-ria, Monte Carlo simulations for the pd

→ (

3_He-

_η

₎

(4)

Fig. 3. The dependenceofdeterminedeventscountonQ3Heηfor pd→3He2γ reaction(leftpanel)andpd→3He6γ reaction(rightpanel).Theerrorbarsincludeboth

statisticalandsystematicuncertainties.

Fig. 4. The eﬃciency for different reactions when applying selection criteria deﬁned for the pd→3_He2_γ _{(left) and pd}_→3_He6_γ _{(right) reaction analysis.}

and pd

→ (

3_He-

_η

₎

bound

→

3He6

γ

reactions were performed in

the framework of the spectator model with the assumption of an isotropic distribution of bound η meson decay products in its rest frame. The momentum of the η meson was simulated using the recent model [14] in which the 3_He-

_η

_relative_momentum

distribution was calculated by solving the Klein-Gordon equation assuming the potential of η-nucleus interaction based on Hiyama’s density distribution in 3_{He [}₅₀_–₅₂_].

For the pd

→ (

3He-

η

)

bound

→

3He2

γ

reaction analysis, the

events containing a 3_{He track in the forward detector and at least}

two photons in the central detector were selected. If there were more than two photons, the pair with the invariant mass closest to the η mass corrected by Q3_He_{η value} was chosen. Then the

restrictions on 3_He_missing_{mass, γ}_-

_γ

_missing_mass,_{and γ}_-

_γ

invariant mass were applied using selection ranges based on the simulated distributions [45]. The excitation function obtained for the pd

→

3_He2

_γ

_{reaction is shown in the left panel of Fig.}₃_.

The signal from the bound state is expected for excess energies around or below zero. The increase of events above 10 MeV is due to the pd

→

3_He

_η

_{reaction. It starts at 10 MeV because of a}_hole

for the COSY beam in the geometrical acceptance of the WASA-at-COSY detector (see Fig.4).

For the pd

→ (

3_He-

_η

₎

bound

→

3He6

γ

reaction analysis, the

events containing a 3_{He track in the forward detector and at least}

six photons in the central detector were selected. For each combi-nation forming three pairs, to identify the η

→

3

π

0

_→

₆

_γ

_decay,

the following quantity is calculated:

D

=

3

i=1

(

mγ(2i−1)γ2i

−

mπ0

)

2 ₍₁₎

where mγ(2i−1)γ2i is the γ pair invariant mass and mπ0 is π 0 _mass.

The combination of six photons that minimises D was chosen. Then analogous to the 2

γ

case, the selection conditions on the

3_{He missing mass, 6}

_γ

_{invariant mass, and 6}

_γ

_{missing mass were}

applied based on the simulated distributions [45]. The excitation

Fig. 5. Excitation curvesdetermined forthe pd→ (3_He-_η₎

bound→3He2γ (upper panel) and pd→ (3_He-_η₎

bound→3He6γ (lowerpanel) reactions. Superimposed linesindicateresultoftheﬁtoftheline.Thepointsabovetheηproduction thresh-oldareexcludedfromtheanalysis.

function obtained for the pd

→

3He6

γ

reaction is shown in the right panel of Fig.3.

The excitation curves have been normalised using the inte-grated luminosity values calculated based on the pd

→

ppnspectator

reaction and the eﬃciency determined based on Monte Carlo sim-ulations. The results for both studied reactions are shown in Fig.5.

(5)

Fig. 6. Exemplary resultofthesimultaneousfitoffunctions (2) and(3) tothe ex-perimentaldatafortheassumedBs andvaluesasindicatedabovethefigures. Superimposedblacklineshowsthe fullfitresult, andthe greenlineshowsthe backgroundfunctiononly.

4. Theupperlimitforthe

η

mesic3_{He production}_cross_section The excitation curves obtained in the analysis (Fig. 5) did not reveal any resonance-like structures and the ﬁt with linear func-tions results in χ2 _{value <}_{1 when normalized to the number of}

degrees of freedom. This indicates that no strong signal from the bound 3_He-

_η

_{state is observed.}

Further on, for the quantitative estimates of the upper limits for the bound state production, a ﬁt to the excitation curves with a linear function (for background) plus a Breit-Wigner function (for the signal) was performed. The ﬁt was done for different com-binations of the assumed η-mesic 3_He_binding_energies_B

s and

widths . The value of was tested in the range from 1.25 MeV to 38.75 MeV (with the step of 2.5 MeV) and Bsin the range from

1.25 MeV to 63.75 MeV (with the step of 2.5 MeV).

For a given Bs and

pair, the following functions were ﬁt

si-multaneously for the two studied reaction channels:

ρ

3f it_He2_γ

(

Q3Heη

)

=

Pη→2γ

· σ

b

(

Q3_He_η

)

+

p1Q3_He_η

+

p2

,

(2)

ρ

3f it_He6_γ

(

Q3Heη

)

=

Pη→6γ

· σ

b

(

Q3_He_η

)

+

p3Q3_He_η

+

p4

.

(3)

Here σ, p1, p2, p3, and p4 are the free ﬁt parameters, Pη→2γ and Pη→6γ are

the

branching ratios for the η

→

2

γ

and η

→

6

γ

de-cays. Assuming that the ratio of branching ratios for the η

→

2

γ

and η

→

3

π

0 _decay_channels_for_the_{bound η} _meson_remain

the same as in vacuum, the vacuum branching ratio values of Pη→2γ = 0.3941 and Pη_→3π0_→₆_{γ = 0.3268} were used for

per-forming the ﬁt [12]. The function σb

(

Q3_He_η

)

in the ﬁt formulae

represents a Breit-Wigner shape which for a given values of Bs

and reads:

σ

b

(

Q3_He_η

,

Bs

,

)

=

σ

2

/

4

(

Q3_He_η

−

Bs

)

2

+

2

/

4

.

(4)

Example results of the ﬁt are shown in Fig.6. The ﬁgure shows re-sults for the Bsand values (indicated above the plots) for which

Fig. 7. Upper limits for the bound state production cross section via pd→

(3_He-_η₎

bound→3He(η decays) as function of binding energy for ﬁxed width =28.75 MeV.ThevaluesoftheBreit-Wigneramplitude σ areshown with sta-tistical uncertainties.Therangeofpossibleboundstateproduction crosssection obtainedbasedonstatisticaluncertaintycorrespondingto90% conﬁdencelevelis shownbybluelines.Therangeofpossibleboundstateproductioncrosssection includingsystematicuncertaintyisshownbygreenlines.

the fitted values of σ differ from zero with the largest statistical significance. Fig.7indicates the results of the fit as a function of the Bs for the most promising value of

=

28.75 MeV.

The upper limit of the total cross section was determined based on the ﬁt parameter uncertainty

σ

stat_:

σ

C L=90%

upper

(

Bs

,

)

=

σ

+

k

σ

stat

,

(5)

where k is

the statistical factor equal to 1.64 corresponding to 90%

conﬁdence level as given in PDG [12]). Fig.7shows the systematic limits (blue lines) in addition to the statistical uncertainties (green lines). Systematic errors were estimated by changing the parame-ters of all cuts applied in the data analysis, and changing the values of assumed potential parameters for the 3_He-

_η

_{interaction that}

de-termines the Fermi momentum distribution for relative motion in the bound state. The highest contribution to the systematic error is connected with the background ﬁt function. The uncertainty due to the ﬁt of quadratic or linear function estimated as σquad

−

σ

lin

varies from about 2 to 5 nb.

In the obtained excitation functions one can see a slight sig-nal from the possible bound state for

>

20 MeV and Bs

∈

[

0

;

15

]

MeV corresponding to the optical potential parameters

−

100 <V0

<

−

70 MeV and

|

W0

|

>

20 MeV in the model

de-scribed in [14]. The result is also consistent with the QMC pre-diction of a potential depth about -100 MeV at nuclear matter density [13] and with the models in Refs. [19,20,22,23]. The al-lowed V0-W0 area is however different to those deduced from

the η-4_{He system [}₅₄_{] using the optical model of Ikeno et al. [}₅₃_]

where most of the model parameter space was excluded allow-ing values of the real and imaginary parts of the potential only between zero and about -60 MeV and -7 MeV respectively. How-ever, the observed signal is within the range of the systematic uncertainty. Hence one cannot make deﬁnite conclusions whether

η

-mesic 3_{He exists with the decay mechanism studied here.}

5. Conclusions

The analysis of the pd

→

3He2

γ

and pd

→

3He6

γ

reactions has been performed in order to search for the existence of an

η

-mesic 3_He_state._The_analysis_of_the_obtained_excitation

func-tions for the pd

→

3He2

γ

and pd

→

3He6

γ

reactions shows slight indication of the signal from the bound state for >20 MeV and

(6)

η

meson. The upper limit is much lower than the limit of 70 nb for pd

→ (

3_He-

_η

₎

bound

→

3He

π

0 reaction obtained by the

COSY-11 Collaboration [55] and is comparable with the upper limits obtained for the dd

→ (

4He-

η

)

bound

→

3Hen

π

0 and dd

→

(

4He-

η

)

bound

→

3Hep

π

− reactions [9]. The much improved

con-straint will help tuning theoretical modelling of the η-nucleon and

η

-nucleus interactions. Acknowledgements

We acknowledge the support from the Polish National Sci-ence Center through grant No. 2016/23/B/ST2/00784, and from the Foundation for Polish Science through the MPD and TEAM POIR.04.04.00-00-4204/17 programmes. Theoretical parts of this work was partly supported by the Faculty of Science, Universi-dad de los Andes, Colombia, through project number P18.160322. 001-17, and by JSPS KAKENHI Grant Numbers JP16K05355 (S.H.) in Japan.

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