CLAS g10 Analysis : Differential Cross

Section for φ Photoproduction on Quasi-free

Protons in Deuterium Near Threshhold

H. Gao, K. Kramer, J. Adkins, W. Chen, X. Wu (Duke

University/Triangle Universities Nuclear Laboratory), D. Tedeschi

(University of South Carolina), T. Mibe, K. Hicks (Ohio University), S.

Stepanyan (Jefferson Laboratory)

1

Contents

1 Physics Motivations: Theoretical and Experimental Aspects 4

1.1 Theoretical Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.2 Experimental Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2 Data analysis 8

2.1 Data Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.2 Calculating the Luminosity . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.3 Corrections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.3.1 Momentum Corrections . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.3.2 Photon energy corrections . . . . . . . . . . . . . . . . . . . . . . . 10

2.4 Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.4.1 Initial skimming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.5 Particle Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.5.1 Missing mass cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.5.2 Fiducial Cuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.5.3 Summary of Event Selections . . . . . . . . . . . . . . . . . . . . . 18

2.6 Yield Extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.6.1 Background subtraction . . . . . . . . . . . . . . . . . . . . . . . . 20

2.6.2 Events Below Detector Threshhold . . . . . . . . . . . . . . . . . . 24

2.7 Acceptance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.7.1 Event Generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.7.2 Monte Carlo Simulation . . . . . . . . . . . . . . . . . . . . . . . . 27

2.7.3 Comparisons with data . . . . . . . . . . . . . . . . . . . . . . . . . 28

2.8 Systematic Uncertanties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3 Results and Discussion 34

3.1 Differential Cross-sections for Hydrogen data . . . . . . . . . . . . . . . . . 34

2

3.2 Differential Cross-sections for Deuterium data . . . . . . . . . . . . . . . . 34

3.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3

1 Physics Motivations: Theoretical and Experimen-

tal Aspects

1.1 Theoretical Motivation

In 1990, S. J. Brodsky, I. A. Schmidt and G. F. de Teramond [1] suggested that the

QCD van der Waals interaction, mediated by multi-gluon exchanges, is dominant when

the interacting two color singlet hadrons have no common quarks. In addition Luke,

Manohar and Savage [2], calculated that the QCD van der Waals interaction is enhanced

at low velocity. This finding supports the prediction that a nuclear-bound quarkonium can

be produced in charm production reactions at threshold. It also suggests the possibility

that the structures seen in s10dσ/dt(pp → pp) and the ANN spin correlation at√

s ∼ 5

GeV and large center-of-mass angles [3] can be attributed to ccuuduud resonant states[4].

If these interpretations are correct, then analogous effects could also be expected at the

strangeness threshold.

Brodsky, Schmidt, and de Teramond [1] investigated the nuclear-bound quarkonium

state using a non-relativistic Yukawa type attractive potential V(QQ)A = −αe−µr/r char-

acterizing the QCD van der Waals interaction. They determined the α and µ constants

using the phenomenological model of high-energy Pomeron interactions developed by Don-

nachie and Landshoff [5]. Using a variational wave function Ψ(r) = (γ3/π)1/2e−γr, they

predicted bound states of ηc with 3He and heavier nuclei. Their prediction was confirmed

by Wasson [6] using a more realistic V(QQ)A potential taking into account the nucleon

distribution inside the nucleus.

Similarly, one expects the attractive QCD van der Waals force dominates the φ-N

interaction since the φ meson is almost a pure ss state. It is possible that a φ-N bound

state or resonant state can be formed in some reactions. In photoproduction of φ meson

from a proton target above threshold, the formation of a bound φ-N state is not likely

4

because of the momentum mismatch between the φ and the recoil proton. As such, no

experimental evidence exists on the formation of the φ-N bound state up to now. On the

other hand, such a φ-N bound state could be formed inside a nucleus.

Using the variational method and following Ref.[1] to assume V(ss),N = −αeµr/r, Gao,

Lee and Marinov [8] find that a bound state of φ-N is possible with α = 1.25 and µ = 0.6

GeV. The binding energy obtained is 1.8 MeV. Their results should be compared with

α = 0.6 and µ = 0.6 GeV determined by Brodsky, Schmidt, and de Teramond [1] for

the cc quarkonium. The interaction is expected to be enhanced by (mc/ms)3, i.e., qq

separation cubed, from cc to ss. Since the radius of the φ meson is 0.4 fm [7] twice the

radius of the J/Ψ meson, α = 1.25 is a rather conservative coupling constant to use for the

φ-N interaction. Also, the interaction is expected to have longer range for the φ-N system

than that of the cc-N interaction. Thus, µ = 0.6 GeV used in the variational approach

described above is also conservative for the φ-N interaction. Further, this attractive force

is enhanced inside the nucleus in the quasifree sub-threshold photoproduction kinematics.

Recently, the φ-N bound state has been studied by Huang, Zhang and Yu [9] using

a chiral SU(3) quark model and the extended chiral SU(3) quark model solving the Res-

onating Group Method (RGM) equation. The model parameters used by the authors in

this work provide good description of baryon bound states, deuteron binding energy and

NN scattering phases shifts in their previous work [10, 11]. A φ-N quasi-bound state with

several MeV of binding energy was predicted by the aforementioned extended chiral quark

model plus channel coupling effect.

1.2 Experimental Concept

Experimentally, it is possible to observe the formation of a bound state φ-N in the sub-

threshold quasifree φ photoproduction process. The incoming photon couples to a moving

nucleon inside the nucleus. The φ meson can be produced near rest inside the nuclear

medium in the laboratory frame when the initial nucleon is moving in a direction opposite

5

to that of the incoming photon. The attractive QCD van der Waals force between the φ

meson and nucleons inside the residual nuclear system enhances the probability for the

formation of the φ-N bound state. It is thus possible for a bound state φ-N to be formed

inside the nucleus in the quasifree subthreshold φ production process from a nuclear

target.

The experimental search for such a bound state would be a triple coincidence detection

of kinematically correlated K+, K−, and proton in the final state. To identify clearly the

signal of a φ-N bound state, one needs to investigate the background contribution to the

K+K−p final state carefully. The dominant background contribution to the signal of

interest are the quasifree subthreshold production of φ meson from a bound proton and

the subsequent decay of φ into K+K−, and the direct production of K+K− from a bound

proton inside the nucleus. The momentum distributions of these final state particles

are expected to be different from those from unbound quasi-free φ production and the

direct quasifree K+K− production. Recently, a detailed Monte Carlo simulation [12] has

been carried out. The Monte Carlo study show that cuts on the momentum correlation

between proton and K+, proton and K−, and on the invariant mass of the K+, K− and

proton system can clearly separate the signal from the decay of a φ-N bound state from

the backgrounds. Therefore, one can identify a bound φ-N state experimentally using

the above mentioned triple coincidence experimental technique. Such an experiment is

feasible [8] at Jefferson Laboratory where advantages of the continuous-wave electron

beam, high luminosity, and the state-of-the-art detector package will be utilized to their

full capabilities.

Recently, high statistics photoproduction data have been collected in CLAS (g10 and

g11) providing high statistic search for exotic θ+ pentaquark state. Such large sample of

data allow analysis of triple coincidence events of K+, K−, and proton. Therefore, it is

ideal to use the deuterium data sample from g10 to investigate the sub-threshold φ meson

production and the direct production of the K+, K−, p final state from a bound proton

6

inside the deuteron. Such a study is important for the following reasons:

• To establish for the first time the subthreshold production of φ meson from a nu-

clear target at the quasifree kinematics (deuteron). The demonstration of such

production is important because future experiment on a dedicated search will rely

on subthreshold φ production at quasifree kinematics.

• The differential cross-section on subthreshold φ production from the bound pro-

ton inside the deuteron at the quasifree kinematics from the g10 data have been

extracted. This information is important to the future search of the φ-N bound

state because it allows for an estimate of the quasifree subthreshold φ production

background.

• The g10 data also allows for a study of the direct γ + “p′′ → K+K−p quasifree

production process from deuteron, which is another important background channel

to the signal from the φ-N bound state.

• This study together with high statistic study of near threshold φ production from

g11 hydrogen data will establish a base line for future search of φ-N bound state

from heavier nuclear targets at sub-threshold kinematics.

7

2 Data analysis

The physical threshold for the γN → φN is 1.57 GeV. However, due to the limitation of

the CLAS acceptance for detecting the three-charged-particle (proton, K+ and K−) final

state, the acceptance weighted threshold is around 1.75 GeV. Therefore, the analysis will

reveal that one can only clearly see φ events in the deuterium data set at energies below

1.75 GeV.

The reaction γd → φp(n) was studied in this analysis. Of the two major decay modes,

φ → K+K− (49%) and φ → K0SK0

L (34%), only the pK+K−(n) was investigated. The

proton, K+ and K− were detected in coincidence. The neutron remained undetected

during the experiment. The quasi-free reaction is selected with cuts on missing mass and

vertex time.

2.1 Data Set

The CLAS g10 data were taken with CLAS with a 24 cm long liquid deuterium target,

with the target cell positioned at 25 cm upstream from the CLAS center. The electron

beam that generated the photon beam used in the experiment had an energy of Ee = 3.8

GeV. The event trigger required at least two charged particles in different sectors. Two

torus settings were used during the experiment a low-field setting (I=2250 A) and a high

field setting (I=3375 A). Approximately equal beam time was given to each setting.

As described in Ref. [21], the stability of the data quality were checked by known

reaction channels. The data files used in this analysis are listed in Ref. [20]. The low

torus field data and high torus field were analyzed seperately and combined after all

corrections (acceptance, luminosity and others) were made.

During the same running period, there were runs made with a liquid hydrogen target.

8

Name Description Value

Nγ Number of photons at the the target From Table Below

ρ density of liquid deuterium 0.163 g/cm3 [19]

A Atomic mass weight 2.0140 [18]

Ltgt Length of the target 24 cm

NA Avogadro Number 6.022× 1023 mol−1 [18]

Table 1: Parameters for luminosity

2.2 Calculating the Luminosity

Nγ, the number of tagged photons in an energy bin, was calculated with the gflux util-

ity [24] based on out-of-time tagger hits from gated trigger TDCs, and clock counts mea-

sured by a scaler, with a correction made for the dead time due to the DAQ processing.

The target density, ρ, was extracted from the information in Ref. [19]. Numerical values

for these parameters are given in Table 1. The integrated luminosity was defined as

L =ρLtgtNA

ANγ = 1.17Nγ barn−1 (1)

where Ltgt is the target length, NA is Avogadro’s number and A is the atomic number for

the target.

The photon energy range studied for extracting the subthreshhold cross-section was

between 1.65 GeV and 1.75 GeV in the deuterium data. The hydrogren data was also used

to study the quality of the cross-section extraction techniques. The number of photons

used in each cross-section is listed in Table 2..

9

Target Torus Field (A) Energy Range (GeV) Nγ

LH2 2250 1.87-2.07 1.56553× 1011 ± 2.2× 107

LH2 2250 2.07-2.32 1.77725× 1011 ± 2.4× 107

LH2 2250 2.32-2.57 8.9641× 1010 ± 2.4× 107

LD2 2250 1.65-1.75 1.257221× 1012 ± 4.1× 107

LD2 3375 1.65-1.75 1.295652× 1012 ± 3.8× 107

Table 2: Number of good tagged photons for each energy bin used for this analysis.

2.3 Corrections

2.3.1 Momentum Corrections

There were two sets of momentum corrections to the g10 data. The momentum of re-

constructed charged particles were corrected for their energy loss in the target region by

ELOSS packages [16, 17]. The additional momentum corrections were applied to correct

for the systematic momentum mis-measurement [15]. The momentum corrections depend

on many kinematic factors and are typically less than 1% for most of the kinematics.

2.3.2 Photon energy corrections

A new calibration for the Hall-B tagger from the pair spectrometer that was documented

in Ref. [23] was used in the analysis. The corrections were typically 0.5% and the accuracy

of the photon energy calibration was estimated as ±0.2%. The run-by-run fluctuation of

the electron beam energy was corrected by N. Baltzell’s table [14]. Typical correction for

the electron beam energy was order of 0.1% and the performance of these corrections has

been checked in the other reactions as seen in Ref. [22].

10

2.4 Event Selection

This section describes the event selections of the pK+K− topology. About 10k events

from φ-meson photoproduction reaction (γp → φp(n)) from a deuterium target were

found from each torus field data set, though only about 100 events in the energy range of

interest between the two sets. The energy distribution of selected φ-meson events from

the pK+K− topology is shown in Fig. 1. A plot of the K+K− invariant mass spectrum

for all photon energies from pK+K− events in the g10 low field deuterium data is plotted

in Fig. 2

Figure 1: Photon energy of selected φ events after background subtraction. The dashed

lines indicate energy range of interest for this analysis of the g10 Low Field deuterium

data.

2.4.1 Initial skimming

A parent sample of the pK+K− topology was skimmed from bos files named kplusneg.

These skimmed bos files were generated in the g10 pass2 cooking processes. The conditions

for skimming were a three charged particle coincidence with a 2 positive and 1 negative

particle.

11

Figure 2: Invariant mass distribution for the K+K− pair in the pK+K− topology after

all the selections. From the g10 Low Field data for deuterium.

2.5 Particle Identification

There were three pieces of information that went into indentifing particles for each event

: charge, Time-of-flight (TOF) mass in EVNT bank and vertex time. The vertex time

for each track was defined as a time traced back from the SC time to the reaction vertex

based on the path length and the momentum of the particle. The vertex time for the

photon was defined as a photon time (RF-corrected tagger time) at the reaction vertex.

The start counter could not be used because if multiple particles hit the same sector

of the start counter the start counter would give incorrect information. This happened

frequently enough that the method only using the SC time was used.

In this analysis, we required that TOF mass given was roughly consistent with the

proton, K+ and K− masses. Good quality flags for tracks were also required at this time.

They were stat > 0, dc_stat > 0 and sc > 0 in the EVNT bank.

An additional requirement for the PID was that the particle vertex time should be

consistent with the photon vertex time. The difference of particle vertex time and photon

12

vertex time were defined as

∆t(γ, K+) = tK+ − tγ, (2)

∆t(γ, p) = tp − tγ, (3)

∆t(γ, K−) = tK− − tγ, (4)

(5)

where

thadron = tSC −LSC

βhadron

+ t0 (6)

tγ = ttagger +Zvertex

c+ t0 (7)

(8)

LSC, Zvertex and t0 are the track path length from the reaction vertex to SC, the z-

coordinate of the reaction vertex and an arbitrary common time offset. The width of

this cut was chosen to be 3σ from the center of the time peak. This was determined

by looking at the signal to signal + background ratio of increasingly tight cuts on vertex

time. The signal to signal + background was determined by fitting a gaussian with a linear

background to the phi-peak with differnt timing cuts on it. The effect of the optimised

cuts on the missing mass squared of the data can be seen in Fig. 3.

2.5.1 Missing mass cut

In addition to the vertex cuts, a cut was made on the square of the missing mass of the

spectator neutron. The signal-to-background ratio in the φ-meson peak was improved by

changing the square of the missing mass cut. In a manner, similar to the vertex timing

analysis, the signal to background ratio was calculated by fitting a gaussian curve with

a linear background to the φ-meson peak in the K+K− invariant mass spectrum. The

missing mass squared cut was altered till the signal to signal + background was optimized.

13

Figure 3: The effect of vertex time cuts on the square of the missing mass. The shaded

area is the square of the missing mass of the events that survive the timing cuts. The top

plot is for hydrogen14

The effect on the K+K− invariant mass peak is shown in Fig. 4. The effect of the missing

mass squared cut on the vertex timing spectrum is shown in Fig. 5.

2.5.2 Fiducial Cuts

The CLAS detector has 6 sectors which have limited acceptence. There are gaps between

the detectors and they do not extend over the entire range of the acceptance. A thorough

investigation of fiducial volume cuts in the CLAS detector was made by T. Mibe [13].

However, it was found that these restricted the amount of statistics for no real benefit

to the systematics. A looser cut was implemented cutting out the areas of greatest

disagreement between Monte Carlo and data.

A minimim scattering angle (θ) cut of 9.0 degrees was made to cut out the beam exit

path. A cut on the azimuthal angle (φ) was also made of ±24 degrees from the center

of each CLAS sector to cut out sections on the edge and between detectors. There is

a section in sector 3 (the sector defined to be centered at 120 degrees) which has some

blockage. Since this is difficult to simulate, this section between 35.0 and 45.0 degrees

scattering angle was cut out entirely. Fig. 6 shows the effect of the fidiciual volume cuts

on positive and negative charged particles respectively.

2.5.3 Summary of Event Selections

Table 3 summarizes the effects of the various good event cuts for the deuterium data.

The cuts listed are accumulated top from bottom. The values of |t − t0| is calculated in

this analysis for the deuterium data in the following manner :

t = (pinit − pfinal)2 (9)

t0 =

[m2

γ −m2p −m2

φ + m2p

2√

s

]2

− (pcminit − pcm

final)2 (10)

s = (pinit + pγ)2 (11)

15

Figure 4: Fits to the φ-meson peak in the K+K− invariant mass spectrum. These fits

were used to calculate a signal-to-background ratio and find an optimal value for the

neutron missing mass squared cut. The value used for optimization is Sig/(Sig + Bkg).

From the g10 low field data for deuterium.

16

Figure 5: The effect of the square of the missing mass cut on vertex time. The shaded

area represent the events that pass through the missing mass squared cut.

17

Figure 6: Plot of scattering angle (θ) versus azimuthal angle (φ) for positive and negative

charged particles in the g10 low field deuterium data set. The left plot are events that

pass the fidiciual volume cut. The right plot are the events rejected by the fiducial volume

cut.

18

Cut Events Survived Events Survived

Low Field High Field

pK+K− skim 576412 439075

Photon Energy 1.65-1.75 GeV 13639 11399

K+K− Inv. Mass 0.999 - 1.029 GeV/c2 479 263

Vertex Timing 165 90

Missing Mass Squared 115 34

Fiducial Volume Cut 101 30

|t− t0| 0.4 - 1.0 (GeV/c)2 (for low) 66 -

|t− t0| 0.7-1.1 (GeV/c)2 (for high) - 14

Table 3: Number of events left after applying each successive cut for low and high field

CLAS g10 deuterium data.

where pinit is the initial proton 4-momentum calculated using the opposite of the missing

momentum of the pK+K− final state, pfinal is the proton 4-momentum in the final state,

pγ is the incident photon 4-momenutm, and mγ, mp and mphi are the mass of a γ (0.0

GeV/c2), proton (0.938272 GeV/c2) and φ (1.019 GeV/c2) respectively [18]. cm indicates

the proton 4-momentum vectors in the center-of-mass frame.

2.6 Yield Extraction

After good pK+K− events are selected, extracting good φ-meson events requires a cut

on the φ-meson mass in the K+K− invariant mass spectrum and subtracting the non-

negligible background events. The good φ-meson events were binned so that the peak

stood out with statistical significance compared to the background.

19

2.6.1 Background subtraction

Since the data sample for the regions of interest is rather small it was found that a

simple sideband subtraction method was adequate for the purposes of this analysis. This

method averaged bins to the left and right of the φ-meson peak in the K+K− invariant

mass spectrum and subtracted it from the events in the central bin. The remaining events

were considered the number of good φ-meson events above background.

Since the φ-meson has a mass of 1.019 GeV/c2 [18], the central bin was from a K+K−

invariant mass from 1.009 GeV/c2 to 1.029 GeV/c2. The left bin was from 0.989 GeV/c2

to 1.009 GeV/c2. The right bin was from 1.029 GeV/c2 to 1.049 GeV/c2. The number

of events were averaged between the left and right bins and subtracted from the middle

bin. The sidebands contain contributions from the Breit-Wigner tails from the φ-meson,

therefore this method requires that when calculating the acceptance the same procedure

be applied to the Monte Carlo data.

We made a comparison between this method, which assumes a linear background,

and a method that assumes a background function that has been suggested by other φ

studies [13] :

f(x) = a√

x2 − (2MK)2 + b(x2 − (2MK)2

)(x > 2Mk) (12)

f(x) = 0 (x < 2Mk) (13)

where x is the invariant mass of K+K− and Mk is the mass of the kaon (0.493277 GeV/c2).

a and b are fit paramters. A Gaussian function with Γ = 0.00425 GeV/c2 and a peak

centered at 1.019456 GeV/c2 was used to fit the data with each of the two background

functions. The Gaussian fit with the non-linear function above results on average of a 5%

smaller amplitude of the non-background part of the function compared to the fit with a

linear background. However, since the statistical error is 25-30% on the good events, the

background will assumed to be linear and a 5% systematic error will just be added to our

results.

20

Target Torus photon |t− t0| range left right center good

Field (A) energy (GeV) (GeV/c)2 bin bin bin events

LH2 2250 1.87-2.07 0.4-0.9 5 3 23 19.0

LH2 2250 2.07-2.32 0.5-0.8 1 3 20 18.0

LH2 2250 2.07-2.32 0.8-1.2 8 5 22 15.5

LH2 2250 2.32-2.57 0.5-1.0 5 7 25 19.0

LH2 2250 2.32-2.57 1.0-1.5 5 4 21 16.5

LD2 2250 1.65-1.75 0.4-0.6 10 8 31 22.0

LD2 2250 1.65-1.75 0.6-1.0 9 14 35 23.5

LD2 3375 1.65-1.75 0.7-1.1 4 1 14 11.5

Table 4: Number of good and background events in each |t − t0| bin. These events pass

both particle identification and fiducial volume cuts.

A listing the number of events for each |t − t0| bin is presented in Table 4. t and t0

are both calculated for a proton target; however, for the case of the deuteron, the final

missing momentum is used to calculate the initial Fermi momentum of the proton. Plots

of the φ photo-production peak are shown in Fig. 7 and Fig. 8. Notice that events at low

photon energy have larger number of events away from the φ peak. This is due to the low

acceptance of the φ peak exaggerating the relative background size.

2.6.2 Events Below Detector Threshhold

Essential to this analysis is the presence of φ photo-production events from deuterium in

kinematic regions favorable to the φ−N bound state. The events that fit this criteria are

those that are only kinematically possible due to the Fermi-motion of the proton in the

nucleus. In practice, the φ-meson events we are looking for are those below the threshhold

of φ-meson photo-production from hydrogen. Due to limitations in the CLAS detector,

the threshhold is at a photon energy of 1.75 GeV. In Fig. 9, we see the comparison of

21

Figure 7: K+K− invariant mass for |t− t0| bins used in this analysis from the CLAS g10

low field (Torus Field setting = 2250 A) hydrogen data. The entries into these histograms

are passed through full particle identification and fiducial volume cuts.

22

Figure 8: K+K− invariant mass for |t− t0| bins used in this analysis from the CLAS g10

low and high field deuterium data. The entries into these histograms are passed through

full particle ID and fiducial volume cuts.

23

deuterium and proton pK+K− photo-production events for photon energies between 1.65

GeV and 1.75 GeV from the CLAS g10 experiment. In addition, there is a historgram of

the same event type for photon energy range 1.6 GeV to 1.75 GeV from the CLAS g11

experiment. There are a substantially more events in the deuterium plot than either of

the plots from the hydrogen data. The number of incident photons for the CLAS g11 data

shown here was 4.316×1012 which is nearly 3× the number of photons for the deuterium

plot. These plots make it apparent that the pK+K− events from the deuterium data in the

photon energy range from 1.65 GeV to 1.75 GeV are below the proton φ photo-production

threshhold in the CLAS detector.

2.7 Acceptance

The calculations for the cross-section depends on accurate estimates of the detector ef-

ficiencies and acceptances for the γp(n) → φp(n) reaction. This section describes the

procedure for determining those quantities.

2.7.1 Event Generator

As input for a simulation of the data, a program written by D. Tedeschi and modified by K.

Kramer generated pK+K− events with physical kinematics consistent with φ production.

The method for doing this was to first generate a pK+K− three-body event based on a

random photon energy chosen from the photon energy range of interest. In the case of

the events generated for the simulation of φ photo-production from quasi-free proton in

deuterium, the fermi motion was simulated by sampling a momentum distribution based

on the Bonn potential. In the case of the production from a hydrogen target, the proton

is assumed to be at rest. The event is then checked to conserve energy and if the t

Mandlestam variable is in the physical region (i.e. t < t0 = t when the center-of-mass

angle between the initial and final state proton momentum direction is 0).

Each event is weighted by the Breit-Wigner shape of the resonance centered at the

24

Figure 9: Invariant mass spectra (in GeV) of K−K+ particles from triple coincidence

detection of the K+K−p particles from CLAS g10 data. The top right panel is from the

hydrogen target and the leftt top panel is from the deuterium target. The bottom left is

from the CLAS g11 experiment on a hydrogen target, but with greater statistics. A cut

which requires the photon energy to be between 1.65 GeV and 1.75 GeV was applied in

all these analyses.

25

φ resonance of 1.019 GeV/c2 and with a Γ = 0.0044GeV/c2. In addition, the events are

weighted by the Y 11 spherical harmonic to represent the p-wave distribution of the reaction

with the z-direction in the direction of the φ-meson momentum. Finally, the following

cross-section weighting is applied :

dσ

dt∝ exp(−b1|t− t0|) (14)

where dσdt

is the differential φ-meson photo-production cross-section with respect to t and

b1 is a fitting parameter.

For the hydrogen data, a fit to the SAPHIR [25] φ-meson photo-production on hy-

drogen cross-section slopes was used. The paper on the SAPHIR φ photo-production on

hydrogen suggests that a b1 = 2.5 (GeV/c)−2 is consistent with their data set. However,

an energy dependent fit of b1 = −1.118 GeV−3/c−2Eγ + 4.815 (GeV/c)−2 seem to match

the |t − t0| dependence of the correponding CLAS g10 hydrogen events. A study of the

acceptance shows that either choice reveals a less than 3% deviation for the cross-section.

A comparison of the g10 hydrogen data and the output of the Monte Carlo simulation is

shown in Figures 10 and 11.

In the deuterium case, where the beam energy is lower than any of the g10 hydrogen

events, the energy dependent fit from the SAPHIR hydrogen data did not produce sim-

ulated results which matched the CLAS g10 deuterium data. In particular, the |t − t0|

distribution of the Monte Carlo was weighted too far towards small |t − t0|. Therefore,

the b1 was modified to a value of 2.1 GeV−2 where the events from the Monte Carlo and

the g10 deuterium data agreed reasonably.

2.7.2 Monte Carlo Simulation

The detector acceptance used to calculate the differential cross-section was calculated

using the events from the above generator. These events were in turn used as input to

CLAS simulation packages GSIM and GPP. The output of these programs was recon-

structed into physics observables with usr_ana. This reconstruction program is the same

26

as used in cooking the data with the exception of some minor changes for handling Monte

Carlo data. These are the standard CLAS simulation packages and have been tested and

examined rigorously.

2.7.3 Comparisons with data

In figures 10, 11, 12 and 13 comparisons of the results of the Monte Carlo simulation and

the CLAS g10 data are shown. The plots were made applying the vertex time and missing

mass cuts for particle identification and the fiducial volume cuts to remove ambiguous

parts of the acceptance. Each histogram is created by averaging histograms created from

the events in the φ sidebands in the K+K− invariant mass spectrum and subtracting it

from the histogram from the central φ peak bin.

Most of the plots show agreement between the Monte Carlo and data within statistical

error. There do seem to be some non-statistical differences, in particular in the proton

data. However, since the cross-section weighting was derived from previous work [25],

no attempts to tweak the parameters of the fit were made. The agreement between

the deuterium simulation and the CLAS g10 data is better due to changes made in the

cross-section weighting.

The acceptances were determined by taking the ratio of simulated events from the

Monte Carlo detector simulation with all particle identification and fiducial volume cuts

applied over the number of events in the same kinematic region from the thrown data

from the event generator. The acceptences for each kinematic in this analysis is listed in

the tables 3.1 and 3.2.

2.8 Systematic Uncertanties

The major sources of systematic uncertainty are from the luminosity and the acceptance

dependence on the cross-section model for deuterium. In previous analysis [13], a com-

parison of the CLAS g6 results and the g10 data found the luminosity could not have

27

Figure 10: Comparison of Monte Carlo simulation and g10 low field hydrogen data. Both

sets of data have had PID and fiducial volume cuts applied. Also all histograms have

undergone background subtraction. Only data from the energy and t range relevant to

this analysis are shown.

28

Figure 11: Comparison of Monte Carlo simulation and g10 low field hydrogen data. Both

sets of data have had PID and fiducial volume cuts applied. Also all histograms have

undergone background subtraction. Only data from the energy and t range relevant to

this analysis are shown.

29

Figure 12: Comparison of Monte Carlo simulation and g10 Low Field deuterium data.

Both sets of data have had PID and fiducial volume cuts applied. Also all histograms

have undergone background subtraction. Only data from the energy and t range relevant

to this analysis are shown.

30

Figure 13: Comparison of Monte Carlo simulation and g10 Low Field deuterium data.

Both sets of data have had PID and fiducial volume cuts applied. Also all histograms

have undergone background subtraction. Only data from the energy and t range relevant

to this analysis are shown.

31

an uncertainty greater than 10%. That analysis does not isolate the systematic error

contribution from the luminosity; therefore, 10% is likely much larger than the actual

uncertainty. This is likely a reasonable number for the purposes of this analysis.

There are multiple sources of uncertainty due to the cross-section model in the event

genertor. Since the t weighting is not well known, varying the b1 parameter in Eq. 14

will change the momentum and angle distributions and therefore the detector acceptance.

This was studied for the deuterium data and found that reasonable variations (±0.5) of b1

could produce an 8% change in the cross-section. In addition, this analysis has assumed

the unpolarized spin density matrix elements were zero. In a study in a separate analysis

by T. Mibe [13] on coherent φ production from deuterium, these parameters can change

the cross-section up to a 10%.

Additional significant sources of error come from momentum/photon energy calibra-

tion of the CLAS package. These can result in 5 MeV shifts in the momentum and missing

momentum. These are estimated to effect the cross-section at the 5% level with the type

of cuts on the data. There is also the 5% systematic error in estimating the background

which is mentioned in the background subtraction section. Additional uncertainty from

factors like error in the branching ratio, number of accidental tracks and background from

the target windows contribute insignificantly to the total systematic error.

The combination of these factors results in a systematic uncertainty of 18% for the

deuterium data. The good agreement between the g10 proton results and the SAPHIR

data suggest that this is a reasonable estimate.

3 Results and Discussion

3.1 Differential Cross-sections for Hydrogen data

Because there are already accurate data on φ photo-production from hydrogen from

the SAPHIR experiment [25], we checked our analysis methods by extracting φ photo-

32

Source of Error % sys. err

Luminosity 10

b1 uncertainty 8

Unpolarized matrix elements 10

Particle Momentum 5

Background Shape 5

Total Systematic Uncertainty 18

Table 5: The systematic errors associated with the extracted cross-sections in this analysis.

production cross-sections from CLAS g10 hydrogen running. The cross-section using the

definition

dσ

dt=

Nφ

εCLASLB∆t(15)

where Nφ is the number of good φ events, εCLAS CLAS acceptance, L is the luminosity,

B is the branching fraction and ∆t is the bin width. In this analysis, a large bin width

was necessary to ensure enough statstics for a meaningful result.

In Table 3.1, the proton results are shown and they are plotted in Fig. 14. Data from

the SAPHIR experiment [25] and the CLAS g10 analysis of pK+ topology [13] are also

shown for comparison. Though there were data taken on the hydrogen target with the

CLAS toroid in its high field setting during the g10 running there were not enough φ

events to make a statistically significant comparison.

The data shows good agreement between the SAPHIR cross-section using a pK+K−

topology and the cross-sections from this analysis. There is disagreement between our

data set and the CLAS g10 pK+ data set in the photon energy range 1.82 to 2.07 GeV

that can’t be explained by stated systematic effects.

33

Figure 14: Comparison of φ photo-production cross-sections from this analysis on g10

hydrogen data and previously published data from the SAPHIR experiement [25]. The

photon energy bins for both the CLAS g10 pK+K− and SAPHIR analysis are identical.

34

γ energy |t− t0| bin mean sim. good stat. dσ/dt stat.

(GeV) (GeV/c)2 (GeV/c)2 acceptance events err. (µ barn/(GeV/c)2) err.

1.87-2.07 0.4-0.9 0.629 0.00314 19.0 5.0 0.155 0.041

2.07-2.32 0.5-0.8 0.643 0.00525 18.0 4.6 0.129 0.033

2.07-2.32 0.8-1.2 0.987 0.00719 15.5 5.0 0.061 0.019

2.32-2.57 0.5-1.0 0.729 0.00515 19.0 5.3 0.166 0.046

2.32-2.57 1.0-1.5 1.229 0.01205 16.5 4.8 0.061 0.018

Table 6: Tabulated results for the φ photo-production cross-section for the CLAS g10

hydrogen data.

3.2 Differential Cross-sections for Deuterium data

The results from the cross-section analysis of the deuterium data is tabulated in Table 3.2

and are plotted in Fig. 15. In the case of deuterium there were enough data in the high field

setting to calculate a cross-section. Using the form of Eq. 14, the fit of the 3 deuterium

points results in a b1 = (2.00± 1.74 (GeV/c)−2). The differential cross-section at t = t0 is

0.21+0.45−0.14 µbarn/((GeV/c)2). While the slope is consistent with our model (2.1 (GeV/c)−2

was the b1 in the event generator) the error is large enough to be consistent with almost

any reasonable value. The differential cross-section at t = t0 has substantial uncertainty

because the cross-section frequently becomes steeper as |t− t0| becomes smaller.

3.3 Discussion

In this analysis, we have extracted the differential φ photo-production cross-section on

deuterium below the production threshhold of lowest photon energy accessible by CLAS

for the hydrogen target. We have also studied the differential cross-section of the g10

hydrogen data to be able to compare our calculations to others. There is good agreement

35

Toroid Current |t− t0| bin mean sim. good stat. dσ/dt stat.

(A) (GeV/c)2 (GeV/c)2 acceptance events err. (µ barn/(GeV/c)2) err.

2250 0.4-0.6 0.497 0.001990 22.0 7.4 0.077 0.026

2250 0.6-1.0 0.787 0.001829 23.5 7.9 0.045 0.015

3375 0.7-1.1 0.887 0.001182 11.5 4.7 0.033 0.013

Table 7: Tabulated results for the φ photo-production cross-section for the CLAS g10

deuterium data. All these points have an initial photon energy in the range of 1.65 GeV

to 1.75 GeV.

Figure 15: φ photo-production cross-section on quasi-free protons in deuterium.

36

between this analysis and the published SAPHIR results; however, there is a discrepancy

between the CLAS g10 pK+ analysis and both of these analyses.

This analysis shows that because these low photon energy events can be seen by the

CLAS detector, φ-meson photo-production from higher Z targets will be also able to be

detected with similar incident photon energy. The cross-sections extracted here will be

considered a background to φ − N bound state searches and estimates in the t range of

this analysis will be useful for putting rough limits on non-bound state background. This

information will pave the way to future φ−N bound state searches.

37

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