Journal of Physics G: Nuclear and Particle Physics

PAPER

Feasibility of studying the resonance using femtoscopyTo cite this article: T J Humanic 2019 J. Phys. G: Nucl. Part. Phys. 46 055001

View the article online for updates and enhancements.

This content was downloaded from IP address 128.146.189.126 on 09/04/2019 at 16:19

https://doi.org/10.1088/1361-6471/ab0b72https://oasc-eu1.247realmedia.com/5c/iopscience.iop.org/401134112/Middle/IOPP/IOPs-Mid-JPGNPP-pdf/IOPs-Mid-JPGNPP-pdf.jpg/1?

Feasibility of studying the K�0ð700Þresonance using π7K0S femtoscopy

T J Humanic

Department of Physics, Ohio State University, Columbus, OH, United States ofAmerica

E-mail: humanic.1@osu.edu

Received 25 October 2018, revised 20 February 2019Accepted for publication 28 February 2019Published 9 April 2019

AbstractThe feasibility of using pKS

0 femtoscopy to experimentally study the *( )K 7000resonance is considered. The *( )K 7000 resonance is challenging to study due toits broad width and proximity in mass to the *( )K 892 , both of which pre-dominantly decay via the πK channel. One of the main interests in the *( )K 7000is that it is considered a candidate for a tetraquark state. It is proposed to usetwo-particle femtoscopic methods with pKS

0 pairs produced in proton–protonand heavy ion collisions assuming a strong final-state interaction betweenthem due to elastic scattering and/or via the *( )K 7000 resonance. Calculationsof pKS

0 correlation functions are made to estimate the strength of these final-state interactions and to see if this signal can be adequately separated from the*( )K 892 background. A possible signature of diquark versus tetraquark

behavior of the *( )K 7000 final-state interaction is also discussed.

Keywords: pKS0, femtoscopy, *( )K 7000 , proton–proton collisions, heavy-ion

collisions

(Some figures may appear in colour only in the online journal)

1. Introduction

The strange *( )K 7000 meson is listed in the 2018 Review of Particle Physics (RPP) with thequalifier ‘Needs confirmation’ [1]. Selected primary information known about it from the RPPis: isospin, =I 1 2, average mass, = ( )m 824 30 MeV700 /c

2, and average width,G = ( ) 478 50 MeV700 /c

2. This information is mostly obtained from experiments that studyheavy particle decays into the kaon-pion channel, which appears to be its primary decaychannel as is also the case for the well-studied *( )K 892 which is nearby in mass [2, 3]. Thebroad width of the *( )K 7000 along with its proximity to the much narrower *( )K 892 make itchallenging to study since it appears as a ‘shoulder’ of the *( )K 892 in the kaon-pion invariant

Journal of Physics G: Nuclear and Particle Physics

J. Phys. G: Nucl. Part. Phys. 46 (2019) 055001 (8pp) https://doi.org/10.1088/1361-6471/ab0b72

0954-3899/19/055001+08$33.00 © 2019 IOP Publishing Ltd Printed in the UK 1

https://orcid.org/0000-0003-1008-5119https://orcid.org/0000-0003-1008-5119mailto:humanic.1@osu.eduhttps://doi.org/10.1088/1361-6471/ab0b72https://crossmark.crossref.org/dialog/?doi=10.1088/1361-6471/ab0b72&domain=pdf&date_stamp=2019-04-09https://crossmark.crossref.org/dialog/?doi=10.1088/1361-6471/ab0b72&domain=pdf&date_stamp=2019-04-09

mass distribution. The main interest in the *( )K 7000 is that its isospin, mass and decay channelfit nicely in the low-mass tetraquark nonet that has been predicted [4, 5]. However, no directand convincing evidence of its tetraquark nature currently exists.

The ALICE collaboration at the Large Hadron Collider has endeavored to experimentallyprobe the quark nature of another of the mesons in the tetraquark nonet, the ( )a 9800 , using KS0K femtoscopy in pp collisions at =s 7 TeV [6] and Pb–Pb collisions at =sNN2.76 TeV [7]. The idea was to study the ( )a 9800 as the final-state interaction (FSI) betweenthe kaons in the KS

0 K pair, the strength of the FSI being related to the quark nature of the( )a 9800 . The authors conclude that their results suggest that the ( )a 9800 is a tetraquark state.The purpose of the present paper is to determine the feasibility of using femtoscopic

methods similar to the ones used by the ALICE collaboration mentioned above in pp andheavy-ion collisions to experimentally study the *( )K 7000 via the pKS0 channel. The pKS0channel is used so that no final-state Coulomb interaction is present between the particles. ThepKS

0 correlation function will be calculated assuming an elastic FSI and a FSI through the*( )K 7000 , both in the presence of the *( )K 892 , to determine the strength of the FSI and the

effect on the FSI signal of the *( )K 892 background. It is assumed in these calculations that thepresence of the *( )K 892 in the femtoscopic correlation function is due only to its directproduction from the collision and is not present as a FSI. It is also assumed that the effect ofthe direct production of the *( )K 7000 on the correlation function is negligible compared withthe FSI effects, as was assumed for the ( )a 9800 by the ALICE collaboration. Theseassumptions are briefly discussed in section 2. A possible signature of diquark versus tetra-quark behavior of the *( )K 7000 FSI will also be mentioned.

2. Calculational methods

The pKS0 correlation function calculated in the present work, *( )C k , is the sum of the FSI

contribution, *( )C kFSI , and *( )K 892 contribution, *¢ ( )( )C k892 , otherwise assuming a flatbaseline,

* * *= + ¢( ) ( ) ( ) ( )( )C k C k C k , 1FSI 892where k* is the momentum of one of the particles in the pair reference frame. The calculationof these contributions is now separately described below.

2.1. FSI contribution to the correlation function

As was done by the ALICE collaboration in their ( )a 9800 studies [6, 7], the femtoscopic FSIcontribution, *( )C kFSI , is calculated with the correlation function from Lednicky and is basedon the model of Lednicky and Lyuboshitz [8, 9] (see also [10]).

** *

**

*

lap

= + + -⎡⎣⎢⎢

⎤⎦⎥⎥( )

( ) ( ) ( ) ( ) ( ) ( )C k f kR

f k

RF k R

f k

RF k R1

1

2

22 2 , 2FSI

2

1 2

where

pº º

-- -( ) ( ) ( ) ( )F z zz

F zz

e erfi

2;

1 e, 3

z z

1 2

2 2

where *( )f k is the scattering amplitude, α is the fraction of p KS0 pairs that come from thep- K0 or p+ K0 system, set to 0.5 assuming symmetry in K0 and K0 production [10], R is theradius parameter assuming a spherical Gaussian source distribution, and λ is the correlation

J. Phys. G: Nucl. Part. Phys. 46 (2019) 055001 T J Humanic

2

strength. The correlation strength is unity in the ideal case of pure FSI, which is assumed inthe present work.

Correlation functions are calculated using two different scattering amplitudes: resonantscattering through the *( )K 7000 , and elastic scattering.

2.1.1. Resonant scattering through the K �0ð700Þ. The equation used for the scatteringamplitude for resonant scattering through the *( )K 7000 was adapted from equation (11) in[10],

**

gg

=- -

( ) ( )( )

f km s ki

, 47002

where, g = G( ) ( ) ( )m k700 700 700 , ( )k 700 is the decay momentum of a daughter in the pair frame inthe *( )K 7000 decay, and * *= + + +p( )s k m k mK

2 2 2 2 20 . For comparison, both the

averaged RPP values for ( )m 700 and G( )700 of 824 and 478MeV/c2, respectively, and values

from [11] of 682 and 547MeV/c2, respectively, were used for calculations, where=( )k 235700 and 104MeV/c, respectively.Note that from equations (2)–(4) it can be seen that FSI effects are largest in the vicinity

of * ~k 0. The *( )K 7000 has kinematic access to this region due to its broad width and thusshould show a strong FSI effect. On the other hand, the K*(892) decay, that peaks atk*∼300MeV/c2 and with a relatively narrow width of Γ(892)=50.3 MeV/c

2 does not haveaccess to the low-k* region and thus FSI effects should not be important for it.

2.1.2. Elastic scattering. For the FSI elastic scattering into isospin state I, the scatteringamplitude equation for s-wave and small k* was used [11],

**

=-+

( ) ( )f k aa k1 i

, 5II

I

where aI is the scattering length for isospin state I. Since there are two possible isospin statesfor pion-kaon elastic scattering, I=1/2 and I=3/2, the scattering amplitude used inequation (2) was taken as the average of the two isospin states [10],

** *

=+

( )( ) ( )

( )f kf k f k

2, 61 2 3 2

where the pion-kaon scattering lengths were taken from [11], =pm a 0.221 2and = -pm a 0.0543 2 .

2.2. K �ð892Þ contribution to the correlation function

The contribution to the π±KS0 correlation function from the decay of the *( )K 892 was cal-

culated assuming a non-relativistic Breit–Wigner function for the pion-kaon invariant massdistribution, dN/dm [12],

pµ

G

- + G( )( )( )

( ) ( )

N

m m m

d

d

1

2 47892

8922

8922

where =( )m 891.76 MeV892 /c2 and G =( ) 50.3 MeV892 /c

2 are the mass and width of the*( )K 892 from the RPP. The contribution to the correlation function from this in terms of k*

can be written as

J. Phys. G: Nucl. Part. Phys. 46 (2019) 055001 T J Humanic

3

**

** *

¢ = =+

++p

⎛

⎝⎜⎜

⎞

⎠⎟⎟( ) ( )( )C k B

N

m

m

kB

N

mk

k m k m

d

d

d

d

d

d

1 1, 8

K

8922 2 2 2

0

where B is a normalization factor. An approximate value for = ´ -B 7.37 10 3 GeV wasobtained from the ALICE experiment that measured * p ( ) KK 892 0 production in 7 TeVpp collisions by estimating the ratio of the unlike-charged particles peak in the vicinity of the*( )K 892 0 mass to the mixed-event background in the raw invariant mass distribution in figure

3 in [12] (B was adjusted to give a *( )K 892 peak at 1.13 in *( )C k when equation (8) is addedto equation (2) in equation (1). The uncertainty in the scale of *¢ ( )( )C k892 resulting from thisprocedure is estimated to be ±15%, which is judged to be sufficient for the present feasibilitystudy.

3. Results

Figures 1–3 show the results for *( )C k from calculations with equation (1) for the *( )K 7000resonant FSI and the elastic scattering FSI. Figures 1 and 2 show results for the *( )K 7000resonant FSI using two different sets of ( )m 700 and G( )700 values, and figure 3 shows results ofusing the elastic scattering FSI. Calculations are shown in each figure for four values of theradius parameter, R=1, 2, 4 and 6 fm. The R=1 and 2 fm calculations represent the typicalsource sizes measured by femtoscopy in pp collisions [6, 13] and the R=4 and 6 fmcalculations represent those typically measured in heavy-ion collisions [7, 14]. The solid(blue) lines represent the full calculation whereas the dashed (red) lines represent thecontribution from *( )C kFSI only, i.e. Equation (2). In each figure the peak of the *( )K 892contribution is located at ∼0.3 GeV/c. Although the scale of *¢ ( )( )C k892 was set using theresults of a 7 TeV pp collisions experiment as described above, it is not expected to changesignificantly with bombarding energy or colliding species [15]. It should also be mentionedthat since an ‘effective range’ calculation was used in deriving equation (2) [8, 9], thecalculations for small R, in particular for R=1 fm, may be somewhat less accurate than forthe >R 1 fm calculations. The uncertainty in *( )C k for the R=1 fm calculations is esti-mated from [6], where ~R 1 fm calculations were also made, to be ~14%, which is judgedto be an acceptable accuracy for the present feasibility study.

In figures 1 and 2 the resonant *( )K 7000 FSI is seen to give an enhancement near * ~k 0that is larger or comparable to the *( )K 892 contribution for R=1 and 2 fm and thendecreasing in size as R increases. It is also seen that the FSI signal overlaps somewhat into theregion of the *( )K 892 for R=1 fm but is well-separated from the *( )K 892 for >R 1 fm. TheFSI produces a ‘dip’ in *( )C k in the k* range 0.1–0.2 GeV/c in both figures for R=1 fm,whereas for >R 1 fm the dip disappears for the RPP mass and width used for figure 1 butbecomes more pronounced and shifts to lower k* for the [11] mass and width used in figure 2.This qualitative difference in the shape of *( )C k between the two mass-width combinationsused suggests that it might be possible to extract information about the mass and width of the*( )K 7000 in femtoscopy experiments.

The elastic scattering FSI used in the calculation of figure 3 gives a qualitatively differentsignal than seen in figures 1 and 2 in that it produces a depletion near * ~k 0 of smallermagnitude than the enhancement produced in the resonant *( )K 7000 FSI case. As also seen forthe resonant *( )K 7000 FSI case, the magnitude of the elastic scattering signal reduces withincreasing R and becomes better separated from the *( )K 892 peak.

With these results, one can now try to evaluate the feasibility of carrying out pKS0

femtoscopic experiments to study the *( )K 7000 in pp and/or heavy-ion collisions. It is

J. Phys. G: Nucl. Part. Phys. 46 (2019) 055001 T J Humanic

4

assumed that an experimental pKS0 correlation function can be constructed that is corrected

for non-flat baseline effects, such as with a Monte Carlo calculation. Looking at figures 1–3, itshould be possible to distinguish between the resonant and elastic FSI cases since they havequalitatively different shapes. Also, the FSI signals are reasonably well-separated from the*( )K 892 peak. If it can be assumed that the resonant and elastic FSI cases are the only

possibilities, a correlation function similar to equation (1) that combines both resonant andelastic FSI cases could be fit to the experimental one, such as

* * * *d d= + - + - - + ¢( ) [ ( ) ] ( )[ ( ) ] ( ) ( )( )C k C k C k C k1 1 1 1 , 9FSIres FSIel 892

where *( )C kFSIres and *( )C kFSIel are the resonant *( )K 7000 and elastic FSI versions of equation (2),and δ is a fit parameter that gives the fraction of each FSI case, i.e. for d = 1 only the resonant*( )K 7000 FSI is present. Looking at equations (2), (4) and (8), other fit parameters could be R,

λ, ( )m 700 , γ and B. Normally in femtoscopic experiments one measures l < 1 due to thepresence of long-lived resonances and non-Gaussian sources [7], resulting in a smaller signalsize than shown in the figures by a factor λ since l = 1 is used in the present calculations

Figure 1. *( )C k with the resonant *( )K 7000 FSI for four R values for for ( )m 700 and G( )700of 824 and 478 MeV/c2, respectively [1]. The solid (blue) line is the full calculationand the dashed (red) line shows the *( )K 7000 FSI component only. The uncertainty inthe scale of the *( )K 892 peak near * ~k c0.3 GeV is estimated to be ±15%.

J. Phys. G: Nucl. Part. Phys. 46 (2019) 055001 T J Humanic

5

(Typically, l ~ 0.5 is measured in femtocopic experiments, e.g. see [6, 7]). Since both theresonant and elastic terms should see these same effects on λ, the same λ could be assumed inboth cases.

The same arguments as used by the ALICE collaboration in considering whether or notthe ( )a 9800 is a tetraquark state can be applied to the *( )K 7000 . If d = 1 for heavy-ioncollisions, this would be consistent with a tetraquark *( )K 7000 since it implies a direct transferof the quarks in the pKS

0 system to the *( )K 7000 [7]. For pp collisions, the pion and neutralkaon are produced in close proximity to each other enhancing the probability for a ddannihilation that would compete with tetraquark formation but enhance a diquark *( )K 7000 .Thus for the pp collision case d = 1 would be consistent with a diquark *( )K 7000 whereas,d < 1 would be consistent with a tetraquark *( )K 7000 (See [6, 7] for a more detailed pre-sentation of these arguments).

It should be noted that sufficient experimental data already exist from RHIC and the LHCto carry out this pKS

0 femtoscopy study proposed above. As an example of this, theexperimental statistics needed would be comparable to those that were used to carry out the

Figure 2. *( )C k with the resonant *( )K 7000 FSI for four R values for for ( )m 700 and G( )700of 682 and 547 MeV/c2, respectively [11]. The solid (blue) line is the full calculationand the dashed (red) line shows the *( )K 7000 FSI component only. The uncertainty inthe scale of the *( )K 892 peak near * ~k 0.3GeV/c is estimated to be ±15%.

J. Phys. G: Nucl. Part. Phys. 46 (2019) 055001 T J Humanic

6

ALICE pp and Pb–Pb collision ( )a 9800 studies [6, 7], and since the publication of thosestudies, more and higher-energy collision data have been taken.

4. Summary

The feasibility of using pKS0 femtoscopy to experimentally study the *( )K 7000 resonance was

considered. The pKS0 correlation function was calculated assuming an elastic FSI and a FSI

through the *( )K 7000 , both in the presence of the *( )K 892 , to determine the strength of the FSIand the effect on the FSI signal of the presence of the *( )K 892 background. It was found thatthe resonant *( )K 7000 FSI is large and qualitatively different in shape compared with theelastic scattering FSI, making it possible to distinguish between the two. It was also found thatthe resonant *( )K 7000 FSI signal is sufficiently well separated from the *( )K 892 peak in thecorrelation function. It is thus judged to be feasible to experimentally carry out such a study.A possible signature of diquark versus tetraquark behavior of the *( )K 7000 FSI that could beapplied in such an experiment was also mentioned. It would be interesting in a follow-up

Figure 3. *( )C k with the elastic scattering FSI for four R values. The solid (blue) line isthe full calculation and the dashed (red) line shows the elastic FSI component only. Theuncertainty in the scale of the *( )K 892 peak near * ~k 0.3 GeV/c is estimated tobe ±15%.

J. Phys. G: Nucl. Part. Phys. 46 (2019) 055001 T J Humanic

7

work to carry out a Monte Carlo simulation to study fitting equation (9) to simulated data todetermine the sensitivity of δ to distinguish between the resonant and elastic cases.

Acknowledgments

The author wishes to acknowledge financial support from the US National Science Foun-dation under grant PHY-1614835.

ORCID iDs

T J Humanic https://orcid.org/0000-0003-1008-5119

References

[1] Tanabashi M et al (Particle Data Group Collaboration) 2018 Review of particle physics Phys. Rev.D 98 030001

[2] Ablikim M et al (BES Collaboration) 2011 Observation of charged κ in*y p- > -+ +-( )J K K892 s , * p- >-+ -+( )K K892 s at BESII Phys. Lett. B 698 183–90

[3] Epifanov D et al (Belle Collaboration) 2007 Study of - -> -( ) ( )tau K S pi nu tau decay at BellePhys. Lett. B 654 65–73

[4] Jaffe R L 1977 Multi-quark hadrons. 1. The phenomenology of qqqq mesons Phys. Rev. D 15 267[5] Alford M G and Jaffe R L 2000 Insight into the scalar mesons from a lattice calculation Nucl.

Phys. B 578 367–82[6] Acharya S et al (ALICE Collaboration) 2019 Measuring K KS

0 interactions using pp collisions at=s 7 TeV Phys. Lett. B 790 22–34

[7] Acharya S et al (ALICE Collaboration) 2017 Measuring K KS0 interactions using Pb–Pb collisions

at =s 2.76 TeVNN Phys. Lett. B 774 64–77[8] Lednicky R and Lyuboshits V 1982 Final state interaction effect on pairing correlations between

particles with small relative momenta Sov. J. Nucl. Phys. 35 770[9] Lednicky R 2006 Correlation femtoscopy Nucl. Phys. A 774 189–98[10] Abelev B I et al (STAR Collaboration) 2006 Neutral kaon interferometry in Au+Au collisions at

=s 200 GeVNN Phys. Rev. C 74 054902[11] Pelaez J R and Rodas A 2016 Pion-kaon scattering amplitude constrained with forward dispersion

relations up to 1.6 GeV Phys. Rev. D 93 074025[12] Abelev B et al (ALICE Collaboration) 2012 Production of *( )K 892 0 and f ( )1020 in pp collisions

at =s 7 TeV Eur. Phys. J. C 72 2183[13] Aamodt K et al (ALICE Collaboration) 2011 Femtoscopy of pp collisions at =s 0.9 and 7 TeV

at the LHC with two-pion Bose–Einstein correlations Phys. Rev. D 84 112004[14] Adam J et al (ALICE Collaboration) 2015 One-dimensional pion, kaon, and proton femtoscopy in

Pb–Pb collisions at =s 2.76 TeVNN Phys. Rev. C 92 054908[15] Adam J et al (ALICE Collaboration) 2017 *( )K 892 0 and f ( )1020 meson production at high

transverse momentum in pp and Pb–Pb collisions at =s 2.76 TeVNN Phys. Rev. C 95 064606

J. Phys. G: Nucl. Part. Phys. 46 (2019) 055001 T J Humanic

8

https://orcid.org/0000-0003-1008-5119https://orcid.org/0000-0003-1008-5119https://orcid.org/0000-0003-1008-5119https://doi.org/10.1103/PhysRevD.98.030001https://doi.org/10.1016/j.physletb.2011.03.011https://doi.org/10.1016/j.physletb.2011.03.011https://doi.org/10.1016/j.physletb.2011.03.011https://doi.org/10.1016/j.physletb.2007.08.045https://doi.org/10.1016/j.physletb.2007.08.045https://doi.org/10.1016/j.physletb.2007.08.045https://doi.org/10.1103/PhysRevD.15.267https://doi.org/10.1016/S0550-3213(00)00155-3https://doi.org/10.1016/S0550-3213(00)00155-3https://doi.org/10.1016/S0550-3213(00)00155-3https://doi.org/10.1016/j.physletb.2018.12.033https://doi.org/10.1016/j.physletb.2018.12.033https://doi.org/10.1016/j.physletb.2018.12.033https://doi.org/10.1016/j.physletb.2017.09.009https://doi.org/10.1016/j.physletb.2017.09.009https://doi.org/10.1016/j.physletb.2017.09.009https://doi.org/10.1016/j.nuclphysa.2006.06.040https://doi.org/10.1016/j.nuclphysa.2006.06.040https://doi.org/10.1016/j.nuclphysa.2006.06.040https://doi.org/10.1103/PhysRevC.74.054902https://doi.org/10.1103/PhysRevD.93.074025https://doi.org/10.1140/epjc/s10052-012-2183-yhttps://doi.org/10.1103/PhysRevD.84.112004https://doi.org/10.1103/PhysRevC.92.054908https://doi.org/10.1103/PhysRevC.95.064606

1. Introduction2. Calculational methods2.1. FSI contribution to the correlation function2.1.1. Resonant scattering through the K0*(700)2.1.2. Elastic scattering

2.2. K*(892) contribution to the correlation function

3. Results4. SummaryAcknowledgmentsReferences