Momentum dependence of the phi-meson nuclear transparency

0.25 MB·English

by  M. Hartmann

Momentum dependence of the φ-meson nuclear transparency∗
M. Hartmann,1,† Yu.T. Kiselev,2,‡ A. Polyanskiy,1,2 E.Ya. Paryev,3 M. Bu¨scher,1 D. Chiladze,1,4
S. Dymov,5,6 A. Dzyuba,7 R. Gebel,1 V. Hejny,1 B. K¨ampfer,8 I. Keshelashvili,9 V. Koptev,7,§
B. Lorentz,1 Y. Maeda,10 V. K. Magas,11 S. Merzliakov,1,6 S. Mikirtytchiants,1,7 M. Nekipelov,1
H. Ohm,1 L. Roca,12 H. Schade,8,13 V. Serdyuk,1,6 A. Sibirtsev,5 V. Y. Sinitsyna,14 H. J. Stein,1
H. Stro¨her,1 S. Trusov,8,15 Yu. Valdau,1,16 C. Wilkin,17 P. Wu¨stner,18 and Q.J. Ye1,19
1Institut fu¨r Kernphysik and Ju¨lich Centre for Hadron Physics,
2 Forschungszentrum Ju¨lich, D-52425 Ju¨lich, Germany
1 2Institute for Theoretical and Experimental Physics, RU-117218 Moscow, Russia
0 3Institute for Nuclear Research, Russian Academy of Sciences, RU-117312 Moscow, Russia
2 4High Energy Physics Institute, Tbilisi State University, GE-0186 Tbilisi, Georgia
5Physikalisches Institut, Universita¨t Erlangen-Nu¨rnberg, D-91058 Erlangen, Germany
n
6Laboratory of Nuclear Problems, Joint Institute for Nuclear Research, RU-141980 Dubna, Russia
a
J 7High Energy Physics Department, Petersburg Nuclear Physics Institute, RU-188350 Gatchina, Russia
8Institut fu¨r Kern- und Hadronenphysik, Helmholtz-Zentrum Dresden-Rossendorf, D-01314 Dresden, Germany
7
9Department of Physics, University of Basel, CH-4056 Basel, Switzerland
1
10Research Center for Nuclear Physics, Osaka University, Ibaraki, Osaka 567-0047, Japan

] 11Departament d’Estructura i Constituents de la Mat`eria and Institut de Ci`encies del Cosmos,
x Universitat de Barcelona, E-08028 Barcelona, Spain
e 12Departamento de F´ısica, Universidad de Murcia, E-30071 Murcia, Spain
- 13Institut fu¨r Theoretische Physik, TU Dresden, D-01062 Dresden, Germany
l
c 14P. N. Lebedev Physical Institute, RU-119991 Moscow, Russia
u 15Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, RU-119991 Moscow, Russia
n 16Helmholtz-Institut fu¨r Strahlen- und Kernphysik, Universita¨t Bonn, D-53115 Bonn, Germany
[ 17Physics and Astronomy Department, UCL, London WC1E 6BT, United Kingdom
1 18Zentralinstitut fu¨r Elektronik, Forschungszentrum Ju¨lich, D-52425 Ju¨lich, Germany
v 19Physics Department, Duke University, Durham, NC 27708, USA
7 (Dated: January 18, 2012)
1
TheproductionofφmesonsinprotoncollisionswithC,Cu,Ag,andAutargetshasbeenstudied
5
via the φ → K+K− decay at an incident beam energy of 2.83 GeV using the ANKE detector
3
. system at COSY. For the first time, the momentum dependence of the nuclear transparency ratio,
1 thein-mediumφ width,and thedifferentialcross section for φmeson production at forward angles
0
have been determined for these targets over the momentum range of 0.6-1.6 GeV/c. There are
2
indications of a significant momentum dependence in the value of the extracted φ width, which
1
corresponds to an effectiveφN absorption cross section in therange of 14-21 mb.
:
v
i PACSnumbers: 13.25.-k,13.75.-n,14.40.Df
X
r
a INTRODUCTION restorationwould be characterizedby a reduction of the
scalar quark condensate in the medium compared to its
magnitude in vacuum.
The study of the effective masses and widths of light
vector mesons ρ, ω, φ in a nuclear medium, through The natural width of the φ(1020) meson is only
their production and decay in the collisions of photon, 4.3 MeV/c2, which is narrow compared to other nearby
hadron and heavy–ion beams with nuclear targets, has resonances. It is therefore the optimal probe for the in-
received considerable attention in recent years (see, for vestigationofmediummodificationsbecausesmalleffects
example, [1–3]). This interest in the in-medium proper- should be experimentally observable. However, this me-
ties was triggered by the hypothesis of universal scaling son is of interest for other reasons. Since the φ is an al-
of Brown and Rho [4], as well as by the QCD-sum-rule- mostpuress¯state,theOkubo-Zweig-Iizuka(OZI)rule[6]
based prediction of Hatsuda and Lee [5] that the masses suppresses quark exchange in its interaction with ordi-
of these mesons should be lower in nuclear matter due nary (non-strange) baryonic matter. Gluon exchange,
to the partial restoration of chiral symmetry in hot and whichplaysasubstantialroleinhigh-energyinteractions
dense nuclear matter. This is a fundamental symmetry between hadrons, is therefore expected to dominate φN
of QCD in the limit of vanishing quark masses and its scattering at all energies [7]. The φ might therefore be
2
consideredas a clean system for the study of gluonic ex- σ is also significantly larger than the ≈ 10 mb ob-
φN
change which, at low energies, should manifest itself as tainedfrombothphotoproductiondataonhydrogen,us-
anattractiveQCDvanderWaalsforce,whichcouldeven ingthevector-mesondominancemodelinthephotonen-
lead to the formation of φN bound states [8]. Secondly, ergyrangeE <10GeV[18,20],andthe additivequark
γ
owing to the small energy release in the dominant KK¯ model [21].
decay channel, any changes in the φ properties are very Values of the in-medium σ were alsodetermined by
φN
sensitive to possible in-medium modifications of kaons the CLAS collaboration from transparency ratio mea-
and antikaons, a subject which is also of great current surementsatJLab[16]. Inthisexperiment,theφmesons
interest. were photoproduced on 2H, C, Ti, Fe, Pb targets and
The main modification of the φ properties in nuclear detected via their e+e− decay mode. From an analysis
matterisexpectedtobeabroadeningofitsspectralfunc- of the transparency ratios normalized to carbon within
tion, while its mass should be hardly shifted [3, 5, 9–12]. a Glauber model, values of σ in the range of 16-
φN
Dileptons from φ → e+e−/µ+µ− decays experience no 70 mb were extracted for an average φ momentum of
strong final-state interactions in a nucleus. Any broad- ≈ 2 GeV/c. These are to be compared to the free value
eningofthe φline-shapeinthe nuclearmattershouldbe of ≈10 mb.
directlytestablebyexaminingdileptonmassspectrapro- The SPring-8 [15] and JLab [16] results are consistent
duced by elementary or heavy-ion beams, provided that with the JLab measurements of coherent [7] and inco-
thenecessarycutsareappliedatlowφmomenta[13,14]. herent [22] φ photoproduction from deuterium. The co-
However,themeasurementofsuchspectraisdifficultdue herent data suggest that σ ≈ 30 mb together with
φN
to the low branching ratios for leptonic decays. Fur- a larger slope for elastic φN scattering compared to
thermore, their sensitivity to in-medium modifications γN → φN [7]. A combined analysis of coherent and
will be reduced by the profile of the nucleus spanning incoherentφ meson photoproductionfromdeuterium fa-
all densities from zero to normal nuclear matter den- vors σ >20 mb [22].
φN
sity ρ0 = 0.16 fm−3, which smears out any density- Whereas medium modifications of σφN might offer a
dependent signal [3]. The KEK-PS-E325 collaboration plausible explanation of the SPring-8 [15] and JLab [16]
measured e+e− invariant mass distributions in the φ re- data,theycanhardlyaccountforthelargevaluefoundin
gion in proton-induced reactions on carbon and copper deuterium. Nuclear density effects are here minimal and
at12GeVandreportedamassshiftof3.4%andawidth other mechanisms, beyond medium modifications, could
increase by a factor of 3.6 at density ρ0 for φ momenta bemoreimportant[22]. Inthiscontextitshouldbenoted
around 1 GeV/c [13]. that the LEPS collaborationrecently studied incoherent
Analternativewaytodeterminethein-mediumbroad- φ photoproductionfromdeuterium at forwardangles for
ening of the φ meson has been proposed in [12] and E =1.5-2.4 GeV [23]. The nuclear transparency ratio,
γ
adopted in [15, 16]. Here, the variation of the φ produc- extractedasafunctionofE ,showsasignificant25-30%
γ
tion cross section (or nuclear transparency ratio) with reduction, which is consistent with that previously de-
atomic number A has been studied both experimentally duced by the same collaborationfromthe A-dependence
and theoretically. The big advantage of this method is ofthisratioforheaviernucleartargets[15]. Ontheother
that one can exploit the dominant K+K− branching ra- hand, very recent data on incoherent φ photoproduction
tio(≈50%). TheA-variationdependsontheattenuation on deuterium, taken by CLAS collaboration in a simi-
of the φ flux in the nucleus which, in turn, is governed lar photon energy range but over a region of larger mo-
by the imaginary part of the φ in-medium self-energy or mentum transfers [24], are inconsistent with the LEPS
width. In the low-densityapproximation[17], this width results [23].
canberelatedtoaneffectiveφN absorptioncrosssection The divergent conclusions drawn from the various ex-
σφN,thoughthisislessobviousathigherdensitieswhere periments emphasize the need to improve our under-
two-nucleon effects might be significant. standingoftheφN interactioninnuclei. Withtheaimof
A large in-medium φN absorption cross section of furthering these studies, we have measured the inclusive
about 35 mb was inferred in a Glauber-type analysis by productionofφmesonsatforwardanglesinthecollisions
the LEPS collaboration from measurements of K+K− 2.83 GeV protons with C, Cu, Ag, and Au targets. The
pairs photoproduced on Li, C, Al and Cu targets at meson was detected via the φ → K+K− decay using
SPring-8foraverageφmomenta≈1.8GeV/c[15]. Simi- the ANKE-COSY magnetic spectrometer [25]. Values
larconsiderationsweregivenin[18]. ThislargeφN cross of the nuclear transparency ratio normalized to carbon,
section was confirmed in BUU transport model calcula- R=(12/A)(σA/σC), were deduced, averagedover the φ
tions [19]. In the low-density approximation, this im- momentum range 0.6-1.6 GeV/c. Here σA and σC are
plies an in-medium φ width of about 110 MeV/c2 in its inclusive cross sections for φ production in pA (A= Cu,
rest frame at density ρ for the conditions of the KEK Ag, Au) and pC collisions in the angular cone θ < 8◦.
0 φ
measurements[13]. Thisisclearlyincompatiblewiththe Thecomparisonoftheratiowithmodelcalculations[26–
width reported in the KEK experiment. This value of 28] yielded an in-medium φ width of 33-50 MeV/c2 in
3
the nuclear rest frame for an average φ momentum of the φ momentum increases.
1.1 GeV/c for normal nuclear density ρ . Each momentum bin contains roughly equal numbers
0
Becauseofthelargenumberofreconstructedφmesons of events and the associated statistical uncertainty in R
for each target (7000-10000), the data could be put in is about 6-7%. The main systematic effects arise from
bins in order to obtain differential distributions. This the evaluation of the number of φ falling within a cer-
allows us to carry out more detailed investigations, in tain momentum bin and the overall uncertainty in the
particular of the momentum dependence of the param- relative normalization. The first was estimated by vary-
eters. In this paper we report on the results of further ingthefitparameters,thebinningofthehistograms,the
analysis of the data collected in our experiment [25, 29]. range of fitting, and the order of the polynomial back-
ground. These results are reported in Table I. The rela-
tive normalization uncertainty, which is described in de-
EXPERIMENT AND RESULTS tail in [25, 29], is about 4-6%, depending on the target
nucleus.
A series of thin and narrow C, Cu, Ag, and Au tar- Inordertotestfurtherthemodelcalculations,thedou-
gets was inserted in a beam of 2.83 GeV protons, circu- bledifferentialcrosssectionsforφmesonproductionhave
lating in the COSY Cooler Synchrotron/storage ring of beenevaluatedwithinthe ANKEacceptancewindowfor
the ForschungszentrumJu¨lich, infrontofthe mainspec- each momentum bin ∆p and each nucleus A as
trometer magnet D2 of the ANKE system (see [30, 31]). d2σA 1 NA
φ φ
The ANKE spectrometer has detection systems placed = , (1)
dpdΩ (∆p∆Ω)hε iLA
to the right and left of the beam to register positively φ int
and negatively charged ejectiles which, in the case of φ whereNAisthenumberofφdetectedinasolidangle∆Ω
φ
meson production, are the K+ and K−. Although only and LA is the integratedluminosity for targetA. In or-
int
used here for efficiency studies, forward-going charged der to estimate the averageefficiency for φ identification
particles could also be measured in coincidence. The hε i, the detection efficiency was first evaluated for each
φ
positively charged kaon was first selected using a dedi- nucleusandeachmomentumbin. Forthistheratioofthe
cated detection system that can identify a K+ against a numberofφdetectedtothatdeterminedfromthefitting
pion/proton background that is 105 more intense (com- the K+K− efficiency-corrected invariant-mass distribu-
pare Fig. 2 in [29] and [31, 32]). The coincident K− was tions was calculated on an event-by-event basis. These
subsequently identified from the time-of-flight difference efficiencies were then averaged over the target nuclei for
between the stop counters in the negative and positive each momentum bin. The root mean square deviations
detector systems. of the individual efficiencies from hε i were about 5%,
φ
The accessible range of the φ meson momenta, 0.6 < which is consistent with the statistical uncertainties.
pφ <1.6GeV/c,wasdividedintosixintervalswithabout The efficiency was estimated for each event using
1000mesonsperbin. TheK+K− invariantmassspectra
ε =ε ×ε ×ε ×ε . (2)
measuredinthepA→K+K−X reactionlooksimilarfor φ tel tr acc BR
all four targets and only the results for carbon and gold The track reconstructionefficiency of K+K− pairs ε is
tr
arepresentedinFig.1. Ineverycasethereisaclearφsig- determined from the experimental data. The correction
nalsitting onabackgroundofmainly non-resonantkaon for kaon decay in flight and acceptance (ε ) is deter-
acc
pair production together with a relatively small num- minedasafunctionofthelaboratorymomentumandthe
ber of misidentified events. To study the momentum de- laboratorypolar angle of the φ meson, using simulations
pendence of the transparency ratio R, the numbers of φ andassuminganisotropicφdecayin its restframe. The
eventsfallingwithin eachmomentumbinwereevaluated range-telescope efficiency ε is extracted from calibra-
tel
for the four targets. With this in mind, the mass spec- tion data on K+p coincidences. Finally, ε represents
BR
tra were fitted by the incoherent sum of a Breit-Wigner the branching ratio of the φ→K+K− decay mode.
function with the natural φ width, convoluted with a The integrated luminosity LA is calculated using the
int
Gaussian resolution function with σ ≈ 1 MeV/c2, and a measuredfluxofπ+ mesonswithmomenta≈500MeV/c
polynomial background function. produced at small laboratory angles. Values of the π+
SincetheefficiencycorrectionsintheANKEspectrom- productioncrosssectionsusedat2.83GeVare59.8±7.2
eter are essentially target-independent, after taking the for carbon, 113±15 for copper, 138±19 for silver and
luminosityintoaccount,toagoodapproximationthera- 174±24 mb/(sr GeV/c) for gold (the details are given
tio of the number of reconstructed φ in any bin for a in [33]).
nucleus A to that for carbon corresponds to ratio of the The measured double differential cross section for φ
cross sections for φ production on these targets in the production for the four targets is given in Table II. The
given momentum bin [25]. The resulting transparency statistical uncertainties are about 5% for each momen-
ratios are given in Table I and shown in Fig. 2. For all tum bin and nucleus. The overall systematic uncertain-
the combinations, Cu/C, Ag/C and Au/C, R falls when ties aretypically20%,risingto23%forthe firstandlast
4
nts400 C 0.600 - 0.825400 0.950 - 1.075400 1.200 - 1.325
e
v
E
200 200 200
0 0 0
400 1.00 1.02 1.04 400 1.00 1.02 1.04 400 1.00 1.02 1.04
0.825 - 0.950 1.075 - 1.200 1.325 - 1.600
200 200 200
0 0 0
1.00 1.02 1.04 1.00 1.02 1.04 1.00 1.02 1.04
IM(K+K-) [GeV/c2]
s Au
nt 0.600 - 0.825 0.950 - 1.075 1.200 - 1.325
ve200 200 200
E
100 100 100
0 0 0
1.00 1.02 1.04 1.00 1.02 1.04 1.00 1.02 1.04
0.825 - 0.950 1.075 - 1.200 1.325 - 1.600
200 200 200
100 100 100
0 0 0
1.00 1.02 1.04 1.00 1.02 1.04 1.00 1.02 1.04
IM(K+K-) [GeV/c2]
FIG. 1: Invariant mass distributions of K+K− pairs produced in pC and pAu collisions in the φ momentum bin noted in
GeV/c. Fits to the uncorrected experimental data in terms of an expected φ shape and a physical background are shown by
thesolid lines. The dashed lines are third order polynomial parameterizations of the backgroundsin the region of the φ peak.
momentum bins. The main sources of the systematic ef- DISCUSSION
fects are related to the background subtraction in the
K+K− invariant mass spectra (5-10%), the simulation
of acceptance corrections ε (5-10%), the determina- Tointerpretthe datapresentedhere,areactionmodel
acc
tion of the range-telescope efficiency ε (10%), and the isessentialand,inthesubsequentdiscussion,weconsider
tel
estimation of the integrated luminosity LA (12-14%). three approaches.
int
Model 1: The eikonal approximation of the Valencia
group [26] uses the predicted φ self-energy in nuclear
medium [11, 12] both for the one-step (pN →pNφ) and
two-stepφ productionprocesses,with nucleonand∆in-
5
TABLE I: The measured transparency ratio R in the acceptance window of the ANKE spectrometer for six momentum bins.
The first errors are statistical and the second systematic, which are mainly associated with the fit quality. In addition there
are overall systematic uncertainties in theratios of about 5-6%, coming principally from therelative normalizations.
p [GeV/c] R(Cu/C) R(Ag/C) R(Au/C)
φ
0.600–0.825 0.49±0.03±0.03 0.48±0.03±0.03 0.34±0.02±0.02
0.825–0.950 0.48±0.03±0.04 0.39±0.03±0.03 0.32±0.02±0.02
0.950–1.075 0.48±0.03±0.03 0.39±0.03±0.03 0.31±0.02±0.02
1.075–1.200 0.49±0.03±0.04 0.40±0.03±0.03 0.30±0.02±0.02
1.200–1.325 0.42±0.03±0.03 0.35±0.02±0.02 0.27±0.02±0.01
1.325–1.600 0.41±0.02±0.02 0.31±0.02±0.02 0.24±0.01±0.01
TABLE II: The measured double differential cross section d2σA/(dpdΩ) [µb/(srGeV/c)] for φ production at small angles
φ
(θ ≤ 8◦) for different momentum bins and nuclei. The first errors are statistical and the second systematic, which are
φ
associated withthefitqualityandincludetheuncertaintyintheaveragedetectionefficiencyhε i. Inadditionthereareoverall
φ
systematic uncertainties of about 20-23%. For thedetails, see thetext.
p [GeV/c] C Cu Ag Au
φ
0.600–0.825 9.9±0.4±0.9 26.2±1.3±2.7 43.3±2.0±4.3 58.0±2.4±5.2
0.825–0.950 13.3±0.6±0.8 34.4±1.7±2.4 46.6±2.3±4.0 72.0±3.0±4.0
0.950–1.075 14.5±0.6±1.0 37.3±1.8±2.6 51.0±2.3±4.0 76.8±3.0±4.9
1.075–1.200 15.3±0.7±1.5 40.3±1.8±3.2 55.8±2.7±4.4 76.7±3.1±6.0
1.200–1.325 18.1±0.8±1.0 40.9±2.1±2.6 57.8±2.8±3.4 83.5±3.8±3.4
1.325–1.600 18.7±0.7±0.9 41.4±1.9±1.8 53.1±2.4±2.2 77.2±3.4±2.9
0.6 an effective in-medium φN absorption cross section σ
) φN
Cφ
σ Cu/C that can be related to the φ width Γ within the low-
φ
/
Aφ density approximation.
σ Ag/C
)( Oneofthemajordifferencesbetweenthethreemodels
A0.5
/ Au/C is in the treatment of the secondary φ production pro-
2
1 cesses. In addition, in contrast to model 2, in model 3 a
(
=
R φ mass shift of −22 MeV/c2 at density ρ0 is considered.
0.4 This results in a modest increase of the φ production
cross section in the range of 0.6-1.6 GeV/c.
The results of the calculations of the transparency ra-
tio as functions of the φ momentum are presented sep-
0.3
arately in the three columns of Fig. 3 for the different
models. Curve 1 of model 1 results from using the pre-
dictions [12] for the imaginary part of the φ self-energy
0.2 in nuclear matter. The other curves, corresponding to
0.6 0.8 1.0 1.2 1.4 1.6
calculations with this self-energy multiplied by factors
p [GeV/c]
φ of 0.5, 2 and 4, demonstrate the sensitivity of R to the
valueofthe φwidth. Calculationswithinmodel2shown
FIG. 2: Momentum dependenceof the transparency ratio R,
inthe centralpanelwere performedwith different values
normalized to carbon, for Cu, Ag, and Au targets.
of a momentum-independent width Γ of the φ meson
φ
in its rest frame at density ρ . These values are noted
0
termediate states. (in MeV/c2) next to the curves. Calculations in model
Model 2: Paryev [27] developed the spectral function 3 presented in the right panel were produced using the
approach for φ production in both the primary proton- absorptioncrosssectionσ (inmb)indicated. Forcom-
φN
nucleon and secondary pion-nucleon channels. parison, the values of the experimental transparency ra-
Model 3: The BUU transport calculation of the tios are also shown, but without error bars.
Rossendorf group [28] accounts for a variety baryon- It is seen from Fig. 3 that, for an almost momentum-
baryon and meson-baryon φ production processes. In independent φ self-energy,model 1predicts a steady rise
contrast to models 1 and 2, where φ absorption is gov- ofthe transparencyratioswithlaboratoryφmomentum,
erned by its width, Γ , model 3 describes it in terms of which is inconsistent with the steady fall in the data.
φ
6
0.8 0.8 0.8
Cu/C Cu/C Cu/C
0.5
1
0.6 0.6 300.6
2 73 10
120 20
4 200 30
0.4 0.4 0.4
0.5Ag/C 1.0 1.5 0.5Ag/C 1.0 1.5 0.5Ag/C 1.0 1.5
C)φ 0.6 0.50.6 0.6
σ
A/φ 1 30
σ
( 10
A) 0.4 2 0.4 730.4 15
2/ 120
1 200 30
4
(
=
R
0.2 0.2 0.2
Au/C Au/C Au/C
0.5
0.4 1 0.4 300.4
10
2 73
15
120 25
0.2 4 0.2 0.2
0.5 1.0 1.5 0.5 1.0 1.5 0.5 1.0 1.5
p [GeV/c]
φ
FIG. 3: (Color online) The transparency ratio R for thethreedifferent nuclear combinations asa function of theφ laboratory
momentum. The experimental data, shown in red, are connected with lines to guide the eye. The predictions of the three
theoretical approaches are shown for model 1 (left), model 2 (center), model 3 (right). For the rest of the notations, see the
text.
Any momentum dependence in the results of model 2 approximation, Γ =p ρ σ /E .
φ φ 0 φN φ
is much more moderate but it is clear that in neither
Figure5showsthemeasureddifferentialcrosssections
case can the variation of the Cu/C, Ag/C and Au/C
for φ production as functions of p . The result on the
φ
transparencyratiosbedescribedwithasinglevalueofthe
lightC nucleusincreasesmuchfasterwiththe φ momen-
φ width. The results from model 3 are more promising
tum than for heavier targets, and this is reflected in the
in this respect, since the steady fall in the data can be
variation of the transparency ratio in Fig. 2. The ex-
reproduced with a constant φN absorption cross section
perimental results are compared with the predictions of
of about 15-20 mb.
the models 2 and 3 that use the values of the φ width
and φN absorption cross section shown in Fig. 4. The
By comparing the calculated and measured values of
agreement of both models with the data generally im-
the transparencyratioforthethreetargetcombinations,
proves for larger p though, in the highest momentum
it is possible to determine the weighted average of the φ φ
bin, the results of model 3 lie closer to experiment. One
widthΓ inthenuclearrestframefordensityρ foreach
φ 0
possible reason for this is the introduction of a greater
momentum bin. The results of applying this procedure
number of φ production channels in this model. On the
areshowninFig.4(a)forbothmodel1and2. Model3,as
other hand, both models underestimate strongly the ex-
wellasthe SPring-8[15] andJLab[16]data, aredirectly
perimental data at low p .
sensitivetothevaluesoftheφN absorptioncrosssection φ
that are noted in Fig. 4(b). The values of Γ shown in The models are, of course, sensitive to the relative
φ
Fig.4(a)were,inthesecases,deducedinthe low-density strength of φ production in pp and pn collisions [25].
7
150 clear that the uncertainties in the resulting parameters
]
2
c (a) would be larger than those that use the transparency
/
V ratio because there are then no cancelations, either the-
e
oretical or experimental. However, calculations within
M
these models show that, for p > 1 GeV/c, the produc-
[ φ
b 100 SPring-8 tion cross sections can be described with a φ width of
Γlaφ about 40 MeV/c2 at density ρ , i.e., with a φN absorp-
0
tion cross section of 15-20 mb. These values are consis-
tent with those shown in Fig. 4. At lower momenta, the
calculationsinboth models underestimate the data even
50
if one takes the free value of the φ width or a vanishing
JLab
value for the φN absorption cross section.
Theaboveinconsistenciessuggestthatsomeprocesses,
KEK whose contributions to the φ production cross sections
0 increase for lower φ momenta and with the size of the
b] 0.5 1.0 1.5 2.0 nucleus, are not present in the models. The inclusion
m of additional secondary production reactions, involving
(b)
[
for example ωN → φN [18], as well as processes where
N
φ the φslowsdownduringits propagationthroughthe nu-
σ 40
cleus through elastic and inelastic collisions [35], would
SPring-8
enhancethelow-momentumpartoftheφspectrum. Un-
fortunately, the cross sections for such processes are not
known experimentally and so cannot be introduced reli-
ably.
20
It can be argued that the transparency ratio is less
sensitivetonucleareffectsandsecondaryproductionpro-
JLab
cesses than the production cross section. This may pro-
vide some justification for using the models to extract
the φ width from the experimental transparency ratio
0 over the full momentum range studied. In fact, model 1
0.5 1.0 1.5 2.0
allowsonetodeducevaluesofΓ fromtheA-dependence
p [GeV/c] φ
φ ofR,whilenotmakinganypredictionsforthe φproduc-
tion cross sections.
FIG. 4: (a) In-medium width of the φ meson in the nuclear
AscanbeseenfromFig.4,theapplicationofthethree
restframeatsaturationdensityρ0 asafunctionoftheφmo-
models yields broadly consistent results. The differences
mentum. The points have been evaluated by comparing the
come mainly from the divergent descriptions of the sec-
dataofFig.2withtheresultsofthethreemodelcalculations
shown in Fig. 3(model1– fullsquares, model2–full circles ondary φ production processes. Our findings are not in-
and model 3 – open triangles). Also shown are the results consistent with the KEK result, taking into account the
from the other experiments noted [13, 15, 16]. The solid line uncertainties in both the experiment and in the model-
represents the Γφ calculated on the basis of the predicted φ dependent analysis. The observed growth of Γ with p
φ φ
self-energy in nuclear matter [12]. (b) The φN absorption
is supported by the SPring-8 and JLab data. Note that
cross section. In the case of model 3, this is the parameter
the values ofΓ extractedwithin the three models agree
that is directly determined from the comparison with exper- φ
quitewellwiththosepredictedbytheValenciagroup[12]
iment, whereas for models 1 and 2 it is deduced from the
in-medium φ widths within the low-density approximation. at φ momenta between 0.6 and 0.825 GeV/c but deviate
The SPring-8 [15] and JLab [16] values of the cross section strongly from them at higher p , reaching a magnitude
φ
are also shown. of about 50-70 MeV/c2 at p ≈ 1.5-1.6 GeV/c. It is
φ
worth noting that, taken together, the latest results by
This is experimentally uncertain and a theoretical esti- theCBELSA/TAPS[36]andCLAS/JLab[16]collabora-
mate of the ratio [34] was used within the models. This tions suggestan increase also of the in-medium ω meson
corresponds to the cross section for φ production in pn width with p .
ω
collisions being about four times larger than in pp colli- Ourdatashowsevidenceforamomentumdependence
sions at 2.83 GeV. This point is particularly significant of σ and, as a consequence, our findings are not in-
φN
for the high momentum components. consistentwiththe resultsfromSPring-8andJLab. The
Analternativewaytoestimatethein-mediumφwidth absorption cross section is between 14 and 21 mb in the
orσ wouldbethroughadirectfitoftheabsolutecross p range of 0.6-1.6 GeV/c. This is also in line with the
φN φ
sectionswithintheframeworkofeithermodel2or3. Itis value σ >20 mb deduced by the CLAS Collaboration
φN
8
from a combined analysis of coherent and incoherent φ propagationthrough nuclear matter is crucial.
production from deuterium [22]. In general, φ meson production on hydrogen with ele-
mentary probes is not completely understood at the en-
ergy of our experiment [37, 38] and this should certainly
)]
V/c20 C 50 Cu be improved. It might be interesting to note in this con-
e text that strangeness production in closely related chan-
G 40
r 15 nels might have some influence here [39–41].
s
b/( 30 We wouldlike to dedicate this paper to our friendand
µΩ [10 20 colleague Vladimir Petrovich Koptev, who died in Jan-
d uary. Support from the members of the ANKE Collab-
p 5
d 10 oration, as well as the COSY machine crew, are grate-
σ/
2d 0 0 fully acknowledged. We are particularly appreciative of
0.6 0.8 1.0 1.2 1.4 1.6 0.6 0.8 1.0 1.2 1.4 1.6 the help and encouragement that we received from Eu-
Ag Au logio Oset. This work has been partially financed by the
80
60 BMBF, COSY FFE, DFG, and RFBR.
60
40
40
∗ Based in part on a PhD thesis submitted by one of the
20 authors (AP) toITEP, Moscow.
20
† E-mail: [email protected]
‡ E-mail: [email protected]
0 0
0.6 0.8 1.0 1.2 1.4 1.6 0.6 0.8 1.0 1.2 1.4 1.6 § Deceased
pφ [GeV/c] pφ [GeV/c] [1] R.RappandJ.Wambach,Adv.Nucl.Phys.25,1(2000).
[2] R.S.HayanoandT.Hatsuda,Rev.Mod.Phys.82,2949
(2010).
FIG. 5: Inclusive double-differential cross sections for φ pro- [3] S. Leupold, V. Metag, and U. Mosel, Int. J. Mod. Phys.
ductionatsmallangles,θφ <8◦,inthecollisionsof2.83GeV E 19, 147 (2010).
protons with C, Cu, Ag, and Au targets as functions of the [4] G. E. Brown and M. Rho, Phys. Rev. Lett. 66, 2720
φlaboratory momentum(fullsquares). Theerrorsshownare (1991).
those from Table II added in quadrature. The experimental [5] T.HatsudaandS.H.Lee,Phys.Rev.C46,R34(1992).
data are compared with the predictions of model 2 (dashed [6] S. Okubo, Phys. Lett. 5, 165 (1963); G. Zweig, CERN
lines) and model 3 (solid lines) using, respectively, the cen- Report No. TH-401, 1964; J. Iizuka, Prog. Theor. Phys.
tral values of the φ width and effective φN absorption cross Suppl.37-38, 21 (1966).
section shown in Fig. 4. [7] T. Mibe et al., Phys.Rev.C 76, 052202R (2007).
[8] H. Gao, S. H. Lee, and V. Marinov, Phys. Rev. C 63,
022201R (2001).
[9] E. Oset and A.Ramos, Nucl.Phys. A 679, 616 (2001).
CONCLUSIONS [10] F. Klingl, T. Waas, and W. Weise, Phys. Lett. B 431,
254 (1998).
[11] D. Cabrera and M. J. Vicente Vacas, Phys. Rev. C 67,
The differential cross sections for the forward produc-
045203 (2003).
tionofφmesonsby2.83GeVprotonsincidentonnuclear
[12] D.Cabrera,L.Roca,E.Oset,H.Toki,andM.J.Vicente
targetshavebeenmeasuredattheANKE-COSYfacility. Vacas, Nucl.Phys. A 733, 130 (2004).
The dependence of the transparency ratio on the φ mo- [13] R. Muto et al.,Phys. Rev.Lett. 98, 042501 (2007).
mentum was determined over the range 0.6-1.6 GeV/c. [14] E. Ya.Paryev, Eur. Phys.J. A 23, 453 (2005).
Values of the φ width in nuclear matter were extracted [15] T. Ishikawa et al.,Phys. Lett. B 608, 215 (2005).
by comparing these data with calculations carried out [16] M.H.Woodet al.,Phys.Rev.Lett.105,112301(2010).
[17] C. B. Dover, J. Hu¨fner, and R. H. Lemmer, Ann. Phys.
within the available models. Independent of the model
(N.Y.) 66, 248 (1971).
used for the analysis, the results show evidence for an
[18] A. Sibirtsev, H. W. Hammer, U.-G. Meißner, and
increase of the φ meson width with its momentum. This A. W. Thomas, Eur. Phys.J. A 29, 209 (2006).
wascompletelyunexpectedandrepresentspossiblyasig- [19] P. Muehlich and U. Mosel, Nucl. Phys. A 765, 188
nificant result. (2006).
Sizable excesses have been observedin the numbers of [20] H.-J. Behrend et al.,Nucl. Phys.B 144, 22 (1978).
φmesonsproducedwithmomentabelow1GeV/c. These [21] H. J. Lipkin, Phys.Rev.Lett. 16, 1015 (1966).
[22] X. Qian et al.,Phys. Lett. B680, 417 (2009).
are not reproduced by the models employed and might
[23] W. C. Chang et al.,Phys. Lett. B 684, 6 (2010).
suggest some enhancement in the low mass φN systems.
[24] X. Qian et al.,Phys. Lett. B696, 338 (2011).
In order to get a deeper insight into the momentum de- [25] A. Polyanskiy et al.,Phys. Lett.B 695, 74 (2011).
pendence of the φ meson in-medium width, a better un- [26] V. K. Magas, L. Roca and E. Oset, Phys. Rev. C 71,
derstandingofboth the φ productionmechanismandits 065202 (2005).
9
[27] E. Ya.Paryev, J. Phys. G 36, 015103 (2009). eConf C110613 (2011).
[28] H.Schade, Universityof Dresden,PhD thesis (2010). [34] L. P. Kaptari and B. K¨ampfer, Eur. Phys. J. A 23, 291
[29] M. Hartmann et al., AIPConf. Proc. 1322, 349 (2010). (2005).
[30] S. Barsov et al., Nucl. Instrum. Methods Phys. Res. A [35] P. Muehlich et al., Phys.Rev.C 67, 024605 (2003).
462, 364 (2001). [36] M. Kotulla et al., Phys.Rev.Lett. 100, 192302 (2008).
[31] M.Hartmannetal.,Int.J.Mod.Phys.A22,317(2007). [37] T. Mibe et al., Phys.Rev.Lett. 95, 182001 (2005).
[32] M.Bu¨scher et al.,Nucl.Instrum.Methods Phys.Res.A [38] B.DeyandC.A.Meyer,arXiv:1103.3821[nucl-ex],2011.
481, 378 (2002). [39] B. Dey et al.,Phys. Rev.C 82, 025202 (2010).
[33] A. Polyanskiy et al., in Proceedings of the XIV Inter- [40] S. A. Pereira et al.,Phys.Lett. B 688, 289 (2010).
national Conference on Hadron Spectorscopy, Munich, [41] H. Kohri et al.,Phys. Rev.Lett. 104, 172001 (2010).
2011, edited by B. Grube, S. Paul, and N. Brambilla,