discovering exotic mesons @clas12
TRANSCRIPT
Discovering Exotic Mesons @CLAS12
CLAS collaboration meeting JLab, March 2019
Vincent MATHIEU
Jefferson LabJoint Physics Analysis Center
Joint Physics Analysis Center
2Ordinary and Exotic HadronsOrdinary baryons:
Ordinary mesons
protonneutron
pion
baryon ⇤
⌧ ⇠ 103s stable
⌧ ⇠ 10�10s
⌧ ⇠ 10�8sCC
kaon⌧ ⇠ 10�8s
⌧ ⇠ 10�20s
J/
Exotic matterglueballshybrid mesons
tetraquarks pentaquarks
CD
UC
3Hybrid Mesons Production
hybrid mesons
Ordinary mesons ~J = ~L� ~S
P = �(�1)L
C = (�1)L+S
Meyer and Van Harleem (2010)
Examples of quantum numbers
3Hybrid Mesons Production
hybrid mesons
Ordinary mesons ~J = ~L� ~S
P = �(�1)L
C = (�1)L+S
Meyer and Van Harleem (2010)
Examples of quantum numbersplot: Meyer and Van Harleem (2010)
data: HadSpec; Dudek et al (2010)
3Hybrid Mesons Production
hybrid mesons
Ordinary mesons ~J = ~L� ~S
P = �(�1)L
C = (�1)L+S
Meyer and Van Harleem (2010)
Examples of quantum numbersplot: Meyer and Van Harleem (2010)
data: HadSpec; Dudek et al (2010)
⇡1 ! ⌘⇡, ⌘0⇡, ⇢⇡, b1⇡, . . .
⌘1 ! ⌘⌘0, a2⇡,K1K, . . .
�p ! ⌘⇡��++
�p ! ⌘⇡0p
in P-wave
4
COMPASS Phys. Lett. B740 (2015)
Ebeam = 190 GeVEbeam = 9 GeV
Eta-Pi Production
�p ! ⌘⇡0p ⇡�p ! ⇡�⌘p
π−
p
η, η′
π−
Pp
⌘
p
�
p
⇡0
�
p⇡
⌘
p
“signal”
“background” only “signal” at high energy
4
COMPASS Phys. Lett. B740 (2015)
Ebeam = 190 GeVEbeam = 9 GeV
Eta-Pi Production
�p ! ⌘⇡0p ⇡�p ! ⇡�⌘p
5
�
p⇡
⌘
p
⇡
⌘
p
�
p
Longitudinal Plot
How do we select beam fragmentation ? Boost in the rest frame
p
beamtarget
⌘
⇡
p
beamtarget
⌘
⇡
Pauli et al PRD98 (2018) 065201Shi et al (JPAC) PRD91 (2015) 034007Van Hove NPB9 (1969) 331
6Longitudinal Plotp
beamtarget
⌘
⇡
q1 + q2 + q3 = 0only 2 variables sinceq1 q2q3
radius: q2 = q21 + q22 + q23
longitudinal angle: !
q3 =
r2
3q sin!
q2 =
r2
3q sin
✓! +
2⇡
3
◆
q1 =
r2
3q sin
✓! +
4⇡
3
◆
6Longitudinal Plotp
beamtarget
⌘
⇡
q1 + q2 + q3 = 0only 2 variables sinceq1 q2q3
�
p⇡
⌘
p
⇡
⌘
p
�
p
radius: q2 = q21 + q22 + q23
longitudinal angle: !
q3 =
r2
3q sin!
q2 =
r2
3q sin
✓! +
2⇡
3
◆
q1 =
r2
3q sin
✓! +
4⇡
3
◆
8
8
Longitudinal Plot: Energy EvolutionVan Hove (1969)
K+
K�
p
⌘
⇡�
p
mesons
baryons
⇡+p ! ⇡+⇡0p
⇡�p ! ⇡�⌘p
�p ! K+K�pEbeam = 3.4 GeV Ebeam = 8 GeV
Ebeam = 190 GeV
3− 2− 1− 0 1 2 33−
2−
1−
0
1
2
3
pq
ηq 0π
q
0πη
ηp0πp
GlueX Spring 2017 p0πη → p γ
preliminary
9GlueX Preliminary Results
�p ! ⌘⇡0p �p ! ⌘⇡��++
⇡+p
Courtesy of A. Austregesilo and C. Gleason
⌘
p
�
p
⇡0
⌘�
p
⇡�
�++
not corrected for acceptance
10Measured Intensities
Implicit variables
Beam energy (fixed)momentum transfer (integrated)
invariant mass (binned)⌘⇡
⇡
⌘�
p p
`
polarization angle
decay angles
⌦ = (✓,�)⌘
+O(Q2)
11Observables: Moments of Angular distribution
L 2`max
`max
is the highest non-negligible wave
Extract moments up to
+O(Q2)
11Observables: Moments of Angular distribution
L 2`max
`max
is the highest non-negligible wave
Extract moments up to
+O(Q2)
12Model
VM et al (JPAC), in preparation
R = {a0(980)| {z },⇡1(1600)| {z }, a2(1320), a2(1700)| {z }}
production: natural exchanges a0(980)
a2(1320)
a2(1700)
line shape: Breit-Wigner form
parameters: arbitrary
Small exotic wave, not apparent in the diff. cross. section
⇢ ⇡
⌘�
p p
`
S(+)0 P (+)
0,1 D(+)0,1,2
13Moments
solid lines: S + P + D wavesdashed lines: S + D waves
P- wave apparent in odd moments but not in even moments
more apparent in odd moments than in even moments
a2(1700)
13Moments
solid lines: S + P + D wavesdashed lines: S + D waves
P- wave apparent in odd moments but not in even moments
more apparent in odd moments than in even moments
a2(1700)
14Beam Asymmetries
⌃D =1
P�
RD Ik(⌦)� I?(⌦)d⌦RD Ik(⌦) + I?(⌦)d⌦
⌃4⇡ = fully integrated
⌃4⇡ =|S(+)
0 |2 + |P (+)0 |2 + |D(+)
0 |2P
m |S(+)m |2 + |P (+)
m |2 + |D(+)m |2
by construction [`]0 < [`]1
15Beam Asymmetries
amplitude: production x decay
Beam asymmetry sensitive to reflection through the reaction plane
⌃D =1
P�
RD Ik(⌦)� I?(⌦)d⌦RD Ik(⌦) + I?(⌦)d⌦
use reflection operator = parity followed by 180° rotation around Y-axis
⇡
⌘�
p p
`
✏
15Beam Asymmetries
amplitude: production x decay
Beam asymmetry sensitive to reflection through the reaction plane
⌃y =1
P�
Ik(⌦y)� I?(⌦y)
Ik(⌦y) + I?(⌦y)
use reflection operator = parity followed by 180° rotation around Y-axis
⌃y = ✏(�1)`[`](✏)m
Odd waves change sign!!!
⇡
⌘�
p p
`
✏
20� � 30� 20� � 30�
17
0� � 10� 0� � 10�
only S and D waves S, P and D waves
Beam Asymmetries: ⌃y±��
20� � 30� 20� � 30�
17
0� � 10� 0� � 10�
40� � 50� 40� � 50�
only S and D waves S, P and D waves
Beam Asymmetries:
with an opening angle greater than 30° the observables is not sensitive to the P-wave (with our model)
⌃y±��
20� � 30� 20� � 30�
17
0� � 10� 0� � 10�
40� � 50� 40� � 50�
60� � 70� 60� � 70�
only S and D waves S, P and D waves
Beam Asymmetries:
with an opening angle greater than 30° the observables is not sensitive to the P-wave (with our model)
⌃y±��
20� � 30� 20� � 30�
17
0� � 10� 0� � 10�
40� � 50� 40� � 50�
60� � 70� 60� � 70�
80� � 90� 80� � 90�
only S and D waves S, P and D waves
Beam Asymmetries:
with an opening angle greater than 30° the observables is not sensitive to the P-wave (with our model)
⌃y±��
18Conclusions
⌘
⌃y = ✏(�1)`
Moments of angular distribution and beam asymmetries provides info on wave content and production mechanism
�p ! ⌘⇡��++
�p ! ⌘⇡0p
�p ! ⌘⌘p
�p ! ⌘⌘0p
Current/future applications @GlueX:
Future plan: partial wave analysis
21Frame
`
⇡
⌘�
p p
boost
helicity conservation
between and� `
b1/h1
✏ = �⇢/!✏ = +
[`](✏)m = T1m � ✏T�1�m
Reflectivity basis:
invariant helicity `
Dominant: (✏ = +,m = 1)
T��m ' ��� ,mT��m + . . .
22
X
✏, ``0
mm0
✓2`0 + 1
2`+ 1
◆1/2
✏(�1)mC`0`00L0C
`m`0m0LM [`](✏)�m[`0](✏)⇤m0H1(LM) + Im H2(LM) /
H1(LM) + Im H2(LM) /= 0The model features only positive projections
m0 = m�M
0 6 �m ; 0 6 m0
M > 1
Observables: Moments of Angular distribution
23
�p ! ⌘⇡0p
Courtesy of A. Austregesilo
a0(980)a2(1320)
�+(1232)
Eta-Pi Production@GlueX
data non-corrected for acceptance
23
�p ! ⌘⇡0p
Courtesy of A. Austregesilo
a0(980)a2(1320)
�+(1232)
Eta-Pi Production@GlueX
data non-corrected for acceptance
25
a
b
1
2
3
P
Y
⌘
⇡�⇡�
P + f
High Mass Region
⇡⌘ ⇡⌘0
a
b
1
2
3
P
Y⌘
⇡�a
⇡�
cos ✓GF ⇠ 1 ! ⌘ forward
cos ✓GF ⇠ �1 ! ⌘ backward
a : IGJPC = 1�(0, 2, 4, 6, . . .)++
f : IGJPC = 0+(0, 2, 4, 6, . . .)++
π−
p
η, η′
π−
Pp
⇡⌘ ⇡⌘0
Eta-Pi @COMPASS
L = 1 L = 2
⇡1(1600)? a2(1320)
black: red: (scaled)
⇡⌘0
⇡⌘
Resonance in angular mom. L = 1 ?
L = 4
a4(2040)
COMPASS Phys. Lett. B740 (2015)
28Eta-Pi@COMPASS
0
20
40
60
80
100
120
140
0.5 1.0 1.5 2.0 2.5 3.0
Inte
nsity
mηπ [GeV]
×103
0
10
20
1.4 1.6 1.8 2.0
JPC = 2++
π−
p
η, η′
π−
Pp
A. Jackura et al (JPAC) and COMPASS, PLB779 (2018)
first precise determination ofpole locationa2(1700)
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P -wave D-wave1�+ 2++
⌘⇡
⌘0⇡
⌘0⇡⌘⇡
PRELIMIN
ARY
PRELIMIN
ARY
Exotic wave @COMPASS
On-going analysis: Systematic studies and exploration of the complex plane
arg(1�+)� arg(2++)
a
b
1
2
3
P
Y⌘
⇡�
⇡�
30Exotic wave @COMPASS
a
b
1
2
3
P
Y
⌘
⇡�⇡�
cos ✓GF ⇠ 1 ! ⌘ forward
cos ✓GF ⇠ �1 ! ⌘ backward
⌘⇡
⌘0⇡
Dispersion relation relates the high (exchanges) and the low (resonances) regions
P -wave
32
X =
r3
8(q1 + q2 + 2q3)
Y =
r1
8(q1 + 3q2)
Z = q1Z
YX
123
123
1
23
1
23
q1 + q2 + q3 + q4 = 0
q1
q2q3 q4
AB ! 1234
triangle = 3 q > 0 or 3 q < 0
square = 2 q > 0