Investigating in-medium properties of the $ω$ meson via the $ω\rightarrowπ^0γ$ decay

0.38 MB·English

by  Janus Weil

Investigating in-medium properties of the ω meson via the ω → π0γ decay
Janus Weila,1, Ulrich Mosela, Volker Metagb
aInstitut fu¨r Theoretische Physik, Universit¨at Giessen, D-35392 Giessen, Germany
bII. Physikalisches Institut, Universita¨t Giessen, D-35392 Giessen, Germany
Abstract
We investigate the feasibility of studying in-medium properties of the ω meson in photoproduction experi-
2 mentsviathedecayω →π0γ. WeusetheGiBUUtransportmodeltocomparedifferentmethodsofobtaining
1 in-medium information, such as the invariant mass spectrum, transparency ratio, excitation function and
0
momentum spectrum. We show that the final-state interaction of the pion poses a major obstacle for the
2
interpretation of the invariant mass spectrum. We also demonstrate that the latter three observables are

ct fairly independent of final-state interactions and thus can give access to the ω’s in-medium properties.
O
Keywords:

0
1
1. Introduction latter has the advantage of a much larger branch-
]
h ingratioof8.3%(roughlythreeordersofmagnitude
The in-medium modification of vector-meson
t abovethedileptonchannel),itsuffersfromthefact
l- propertieshasbeenatopicofinterestforquitesome thatofonethedecayproducts(namelytheπ0)un-
c timenow. Theirvacuumpropertiesarewell-known
dergoes strong final-state interactions (FSI). For a
u
nowadays, but the question of how their masses
n long time it was commonly assumed that there are
[ and widths change when embedded in a hadronic ways to cope with this issue, but we will show here
medium (either cold nuclear matter or the hot fire- that the pion FSI poses a major obstacle and in
1
v ballofaheavy-ioncollision)isdebatedheavily. For fact makes the π0γ decay unsuitable for certain in-
recent reviews on in-medium effects, see [1, 2, 3].
4 medium studies.
7 The popular predictions on the one hand in- Experimentally, the decay ω → π0γ has been
0 clude standard many-body effects, like a collisional
studied intensively by the CBELSA/TAPS col-
3 broadening of the meson spectral function due to
laboration in photoproduction reactions on nuclei
.
0 collisions with the hadronic medium. On top of [5, 6, 7, 8]. Moreover, ω mesons in cold nuclear
1 that, a second class of predictions claims that the
matter have been investigated via the dilepton de-
2
vector-meson masses are shifted in the medium
cay channel by CLAS at JLAB [9] and HADES at
1
due to the (partial) restoration of chiral symmetry.
: GSI [10].
v QCD sum rules can constrain these effects, but do
We will start this paper with a short description
i
X not provide definitive predictions [4]. of features of the GiBUU model, which are rele-
Whenstudyingin-mediumeffectsoftheω meson
r vant for the present study of ω photoproduction
a by observing its decay products one has to remem-
reactions on nuclei. This will be followed by an
ber that the invariant mass reconstructed from the
overview over several methods for determining the
four-vectors of the decay products always contains
in-medium properties of ω mesons in cold nuclear
a product of spectral function and branching ratio.
matter. As a new method we propose a study of
In choosing the decay channel one has the choice
the ω meson’s momentum distribution.
between the rare dilepton decay mode, which is
freeoffinal-stateinteractions,andthemorepromi-
nent hadronic decays, like ω → π0γ. While the 2. The GiBUU transport model
Our tool for the numerical simulation of ω pro-
1Email: [email protected] ductionanddecayistheGiBUUhadronictransport
Preprint submitted to Physics Letters B October 12, 2012
model, which provides a unified framework for var- 90
tot.
ious types of elementary reactions on nuclei as well el.
as heavy-ion collisions [11, 12]. This model takes 80 πN
2πN
careofthecorrecttransport-theoreticaldescription
70
of the hadronic degrees of freedom in nuclear reac-
K=2
tions, includingthepropagation, elasticandinelas- 60
tic collisions and decays of particles.
In GiBUU the spectral one-particle phase-space b] 50
m
distributions, F(x,p), of all particles are obtained [N
by solving the coupled Kadanoff-Baym equations σω 40 K=1
[13] for each particle species in their gradient-
30
expanded form [14]
20
DF(x,p)−tr(cid:8)Γf(cid:60)Sret(x,p)(cid:9) =C(x,p) , (1)
pb 10
with 0
0 0.5 1 1.5 2 2.5 3
DF ={p −H,F} . (2) p
0 pb lab
Here {...} denotes a Poisson bracket, and the
pb
so-called backflow term (second term on the lhs of
Figure1: (Coloronline)TotalωN collisioncrosssectionfor
(1)) is usually neglected. Further, f(x,p) is the K=1andK=2.
phase-space density related to F by
γN →ω∆, which have been fitted to experimental
F(x,p)=2πgf(x,p)A(x,p) , (3)
data.
whereA(x,p)isthespectralfunctionoftheparti- The absorption and rescattering of ω mesons in
cle2 andg isthespin-degeneracyfactor. Thequan- nuclear matter proceeds via the channels ωN →
tityΓinthebackflowtermisthewidthofthespec- ωN, ωN →πN, ωN →2πN and ωN →R (where
tral function, and Sret(x,p) denotes the retarded R is a nucleon resonance). It is described in Ap-
Green’s function. pendix B.3 of [11], just like πN scattering, which
Our model explicitly includes off-shell transport reproduces the available data reasonably well. Fol-
of particles with density-dependent spectral func- lowing ref. [16] we introduce an extra modification
tions. Inparticular,equ.(1)iscompatiblewiththe factor K for the inelastic ωN scattering:
off-shellequationsofmotionobtainedin[15],which
leadstothecorrectasymptoticspectralfunctionsof σ˜inel =σinel·K .
ωN ωN
particles when they leave the nucleus. The expres-
ForK >1,theadditionalcontributionstothecross
sion C(x,p) on the rhs of (1) denotes the collision
sections are put into the channel ωN →2πN.
term that couples all particle species; it contains
Fig. 1 shows the total ωN cross section for K =
both a gain and a loss term. For a short derivation
1 and K = 2, as well as the contributions from
ofthistransportequationandfurtherdetailswere-
different channels (for K =1 only).
fer the reader to [11]. In order to solve the BUU
Our simulation procedure uses the full photon-
equation numerically, we rely on the test-particle
energy range of 1.2 to 2.2GeV with the appropri-
ansatz. Here the phase-space densities are approx-
ate 1/E weighting factor of the Bremsstrahlung
γ
imated by a large number of test particles, each
spectrum. Any in-medium changes, such as that of
represented by a δ-distribution in coordinate and
the mass and the width, are assumed to be linearly
momentum space.
proportional to the nuclear density.
The photoproduction of ω mesons is treated as
described in Appendix C.8 of [11], i.e. with pa-
rameterized matrix elements for γN → ωN and 3. Invariant Mass Spectrum
The idea to study in-medium properties of the ω
2Aisnormalizedas(cid:82)0∞A(x,p)dp0=1. mesonviatheπ0γinvariantmassspectrumwasfirst
2
1.6 1.2
1.4 a) vacuum spectral function b) collisional broadening
1
1.2
all π0γ decays 0.8
m0πγ 1 vina-cmueudm. ddeeccaayyss m0πγ
0.8 0.6
d all (no FSI) d
d/σ 0.6 vac. (no FSI) d/σ
in-med. (no FSI) 0.4
0.4
0.2
0.2
0 0
0.6 0.65 0.7 0.75 0.8 0.85 0.6 0.65 0.7 0.75 0.8 0.85
mπ0γ mπ0γ
2 1.8
1.8 c) 16% mass shift 1.6 d) coll. broadening + mass shift
1.6 1.4
1.4
1.2
m0πγ 1.2 m0πγ 1
1
/dσ 0.8 /dσ 0.8
d d
0.6
0.6
0.4 0.4
0.2 0.2
0 0
0.6 0.65 0.7 0.75 0.8 0.85 0.6 0.65 0.7 0.75 0.8 0.85
mπ0γ mπ0γ
Figure 2: (Color online) Calculated π0γ mass spectrum for γ+Nb at 0.9 - 1.3GeV, in four different in-medium scenarios.
Shown are the total spectrum as well as the contributions from in-medium (ρ>0.1ρ0) and vacuum (ρ<0.1ρ0) decays, with
andwithoutpionFSI.
proposed in an early exploratory study by Mess- Moreover, not all of the in-medium decays hap-
chendorp et al. [17], and further studied theoreti- pen at full nuclear density ρ in the center of the
0
cally in a subsequent transport investigation [18]. nucleus. Every nucleus has a diffuse surface with
Thefirstmeasurementfollowedsoon[5]andindeed a slowly dropping density distribution. The frac-
claimedtoobserveashiftedin-mediumpeakinthe tion of ω mesons decaying at the surface will fur-
π0γ invariantmassspectrum. Thisclaimwaswith- ther smear out the in-medium peak, if we expect a
drawnlater,afterfollow-upanalyses[7,8]withsys- density-dependent mass drop. This holds for any
tematicstudiesofthebackgroundcouldnotconfirm decay mode of the ω meson.
the finding. For the π0γ channel, an additional limitation of
The results of our present transport study indi- theusefulnessoftheinvariantmassspectrumasan
cate that about 30 % of all ω → π0γ decays oc- indicator for in-medium effects is the strong final-
cur in the medium (i.e. at densities above a thresh- state interaction (FSI) of the π0 daughter particle.
old of 0.1ρ ). However, there are several effects Mostpreviousstudiesconcentratedonthefactthat
0
which affect the actual observability of any in- thebackgroundcreatedbyrescatteredpionscanbe
mediumeffect. Firstofall,oneexpectsasignificant suppressedbykineticenergycuts[17]. Littleatten-
’melting’ of the in-medium peak due to collisional tion was paid to the fact that the pion FSI selec-
broadening. From the transparency ratio measure- tively favors decays at small densities. If a π0 from
ment of Kotulla et al. [6] a collisional width of an ω decay scatters with a nucleon, there are two
Γ ≈130−150MeVwasextracted,whichexceeds possibilities: Either the collision is inelastic, lead-
coll
theω decaywidthinvacuumbymorethanafactor ing to an absorption of the π0 (π0N → NX), pos-
10. Thismeansthatthein-mediumpeakshouldbe sibly due to charge exchange (e.g. π0p → π+n); or
considerably smeared out, making it much harder the collision is elastic (π0N → π0N), which typi-
to observe [19]. callycausesanenergylossofthepioninthelabora-
3
The density distributions of the production and
decay point (with and without FSI) are shown in
dρ102
n/ fig. 3. While the production density has a clear
d
peakatfullnucleardensity,thedecaypointtendsto
10 <ρ>=0.73ρ0 lie in the vacuum due to the rather long lifetime of
theω meson(τ ≈22fm/c). Ontopofthis, theFSI
93Nb(γ, ω) of the decay pion further decreases the sensitivity
1 to high densities.
E=900 1300 MeV In summary, we conclude that the π0γ decay
γ
<ρ>=0.54ρ channel is clearly inferior for invariant mass anal-
10 1 0 yses compared to e.g. e+e−, mainly due to pion
FSI. Moreover, we note that in general mass spec-
trumanalysesarebettersuitedformoreshort-lived
10 2 <ρ>=0.25ρ
0 mesons(liketheρ),whichhavealargerprobability
of decaying in the medium.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
ρ/ρ
0
4. Transparency Ratio
Figure 3: (Color online) Distribution of the production
pointsofω mesonsinphotoproductiononNbasafunction Another way of investigating the in-medium
of density (topmost line). Also shown are the decay points properties of the ω meson is to measure its absorp-
with(lowest)andwithout(middleline)FSI.
tion as a function of nuclear mass number A. This
method only gives information on the collisional
tory, so that the reconstructed π0γ invariant mass width, but not on a possible mass shift. It does
not require the measurement of actual in-medium
is changed dramatically. In both cases the event
decays,asisthecaseforthemassspectrum,butcan
isbasicallyunusablefortheω reconstruction, since
relycompletelyonthefour-momentaofthefinalde-
the original ω in-medium mass is lost.
cay products in vacuum. However, since pion FSI
The FSI has dramatic consequences for the in-
may decrease the number of finally reconstructed
medium part of the π0γ mass spectrum. Decay
ω mesons the transparency itself does not give di-
products coming from high densities at the center
rectly the attenuation of ω mesons alone, but has
of the nucleus have little chance of making it out-
to rely on state-of-the-art transport calculations to
sidewithoutrescattering,sothatmostlythosefrom
extract the actual in-medium width. Only in the
the surface will be observed, which carry little in-
caseoflargecollisionalwidthsthepionFSIbecome
formation on medium modifications. This means
negligible [20].
thatthepionFSIcutsawaymostofthein-medium
The so-called transparency ratio (normalized to
peak,ascanbeseeninFig. 2,andeveninthevery
12C) is defined as:
unlikely scenario of a pure mass shift, only a minor
in-medium contribution to the spectrum is left. In
the scenarios including collisional broadening, the 12σ
T = γA→ωX . (4)
in-medium peak is already broadened so strongly, A Aσ
γ12C→ωX
thatevenwithoutanyFSIofthedecayproducts,it
wouldbehardtounambiguouslymeasureamedium The first measurement of this quantity was per-
modification of the spectrum and to distinguish it formed by the CBELSA/TAPS collaboration via
from the background. π0γ decaysinphotoproductionexperiments[6]. By
Note that Fig. 2 includes the mass resolution assuming a low density approximation, an inelastic
of the CBELSA/TAPS detector, incorporated by ωN cross section of about 70mb and its momen-
folding the spectrum with a Gaussian distribution tum dependence were deduced from the measured
of 19 MeV width. However, we have verified that transparency.
themassresolutionofthedetectorisnotalimiting More recently, it was claimed in [21] that the
factor,andthatevenanimprovementofthisresolu- CBELSA/TAPS data can be described by a much
tionwouldnotdramaticallyincreasethechancesof lower total ωN cross section on the order of 30mb.
being able to observe any in-medium modification. However, we note that the treatment presented
4
In fact, the ω transparency ratio has also been
1.2
ω → π0γ CNab//CC measured via dilepton decays from photon-induced
reactions on nuclei by the CLAS collaboration
1 Pb/C
at Jefferson Lab [9]. However, their results are
0.8 not compatible with the CBELSA/TAPS measure-
ments and claim an even larger absorption, which
TA 0.6 cannotbeexplainedbyanyofthetheoreticalmod-
els (including ours).
0.4
Moreover, the dilepton data recently measured
bytheHADEScollaboration[10]couldprovidefur-
0.2
therconstraintsontheωabsorptioninnuclearmat-
0 ter. An ω peak has been identified in both pp and
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 pNbreactionsatthesamebeamenergyof3.5GeV.
pω [GeV] However, there are two obstacles for extracting the
ω absorption cross section: First, the ω peak needs
1.2 to be separated from an underlying background
ω → e+e- CNab//CC (mostly due to the ρ meson), whose shape is non-
1 Pb/C trivialalreadyinpp,andmightbefurthermodified
in pNb [22]. Second, only a reference from pp col-
0.8
lisions is available, and the ω production from pn
collisions in not well constrained.
A 0.6
T
0.4
5. Excitation Function
0.2
0
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 It was argued in [16] that the ω excitation func-
pω [GeV] tion, i.e. the total ω photoproduction cross sec-
tion on a nucleus dσ /dE , is sensitive to in-
γA→ωX γ
medium modifications of the ω meson. In partic-
ular, a downward mass shift of the ω in medium
Figure 4: Transparency ratio for three different nuclei rel-
ative to 12C. Top: Obtained via the π0γ decay, with would lower the threshold for ω photoproduction
Tπ > 150MeV, bottom: obtained from the dilepton decay, and increase the cross section due to the enlarged
incomparisontotheπ0γ datafrom[6]. phase space, which could be determined in an exci-
tation function measurement.
Fig. 5 shows the energy-dependent ω photo-
thereassumedafixedphotonenergyof1.5GeV for production cross section on C and Nb (observed
comparisonwiththeCBELSA/TAPSdata,instead through the π0γ decay) for photon energies from
of the full bremsstrahlung energy spectrum used in threshold up to 1.5GeV. While the collisional
the experiment. broadeningscenarioonlyslightlyenhancesthesub-
The results obtained with the GiBUU model are threshold contributions (which presumably would
shown in Fig. 4. To properly describe the data, we be hard to measure, since the cross sections be-
need to modify the inelastic ωN cross section by a come very small there), the scenarios including a
factor of K ≈ 2.0. Our model yields a rather flat mass shift exhibit a much stronger enhancement,
momentum dependence for the π0γ transparency also above the free ω production threshold of Eγ ≈
ratio. Furthermore, it should be noted that the 1.1GeV.
transparencyratioobtainedviadileptondecays(as It is important to note that the modification of
shown in fig. 4 bottom) is mostly compatible with the excitation function is proportional to the den-
the π0γ result, and only shows slight deviations at sityattheproductionpoint,incontrasttothemass
low momenta, which confirms that this observable spectrum modifications discussed above, which are
is not strongly affected by pion FSI. proportional to the density at the decay point.
5
Fig.6showsthemomentumspectrumofaγ+Nb
reaction with photon energies in the range of 0.9 -
10-1 1.3 GeV. Aninvariantmasscutof650MeV<m<
850MeV was used to select the relevant ω mass re-
gion and to remove events with π0 rescattering. It
b]µ γ 12C → π0 γ N X should be noted that the momentum distribution
/A [σ 10-2 is quite sensitive to the angular distribution of the
ω production process. The angular distributions
usedinthesimulationproperlyreproducethemea-
vac
CB surements on the free proton [23, 24]. For better
10-3 CB+shift comparison, the different curves are normalized to
shift
have the same integral. One can see that, while
0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
the collisional broadening scenario is hardly distin-
E [GeV]
γ guishable from the vacuum curve, in the scenarios
involving mass shift the momentum distribution is
clearly shifted (the maximum of the distribution
10-1 shows a clear offset and also the average is shifted
by about 25 - 50 MeV).
/A [b]σµ 10-2 γ 93Nb → π0 γ N X mtheeTnehtxuisimsmtedenaicsnetsraibnthudatmitonaagmnmietigauhsduterebomfeaeunnsteindo-fmttoehdediueπtm0eγrmmmainoses-
shift of the ω meson. Preliminary data [25] seem
vac to indicate that the in-medium scenarios involving
CB mass shifts are disfavored.
10-3 CB+shift
shift
2.5 vac (0.616)
0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
CB (0.619)
E [GeV] CB+shift (0.591)
γ ea] 2 shift (0.559)
ar
o
Figure 5: (Color online) Calculated excitation function for d t
photoproduction of ω mesons in the π0γ decay channel on e 1.5
z
12C and 93Nb nuclei. The different curves represent the ali
samein-mediumscenariosasthoseusedinfig.2. m
or 1
n
p [
6. Momentum Spectrum d
σd/ 0.5
In addition to the previously established meth-
ods discussed in the preceding sections, we propose
0
here a new method for extracting in-medium prop- 0 0.2 0.4 0.6 0.8 1
erties of the ω meson from photoproduction data. p [GeV]
Our simulations show that the momentum spec-
trumofωmesonsproducedonanucleusissensitive
to medium modifications of the ω properties. Figure6: (Coloronline)Calculatedπ0γmomentumdistribu-
This effect is due to the kinematics in the ω pro- tionforγ+NbatEγ =0.9−1.3GeV. Theaveragemomenta
for the different in-medium scenarios are given in brackets
ductionprocess,whichisalteredbytheω’smedium
(inGeV).
modifications. Whenanω isproducedwithalower
mass, then, on average, it’s total energy is lower.
Furthermore, the meson has to come back to its
freevacuummassonitswayoutofthenucleus;the 7. Conclusions
necessary energy is obtained by converting kinetic
energy into mass. This conversion process lowers Wehaveevaluatedvariousapproachesforthede-
the momentum. terminationofin-mediumpropertiesoftheωmeson
6
in cold nuclear matter via the π0γ decay in photo- [19] J. Lehr, M. Effenberger, H. Lenske, S. Leupold,
production experiments. Our analysis shows that U.Mosel,Phys.Lett.B483(2000)324–330.
the lineshape analysis of the π0γ invariant mass [20] M. Kaskulov, E. Hernandez, E. Oset, Eur.Phys.J. A31
(2007)245–254.
spectrum suffers mainly from the hadronic FSI of
[21] T.Rodrigues,J.Arruda-Neto,Phys.Rev.C84(2011)
the pion, which drastically reduces the sensitivity 021601.
to medium modifications. [22] J.Weil,H.vanHees,U.Mosel,Eur.Phys.J.A48(2012)
111.
The transparency ratio on the other hand is a
[23] J. Barth, W. Braun, J. Ernst, K.-H. Glander, J. Han-
reliable approach for determining the ω absorption
nappel,etal.,Eur.Phys.J.A18(2003)117–127.
crosssection. ItisnotassensitivetopionFSI,since [24] M.Williams,etal.,Phys.Rev.C80(2009)065209.
it relies mostly on decays of ω mesons outside the [25] V. Metag, et al., Prog.Part.Nucl.Phys. 67 (2012) 530–
535.
medium. However, it can not make any statement
about an in-medium mass shift of the ω.
Furthermore, we investigated two other methods
of determining the in-medium mass of the ω: the
excitation function and the momentum spectrum.
Both are sensitive to the density at the production
place of the meson, and not at the decay location
(as is the case for the lineshape), which can poten-
tially yield larger effects.
Acknowledgments
Work supported by HIC-for-FAIR, HGS-HIRe
and DFG under TR16. We thank Stefan Friedrich
for the help in producing fig. 3.
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