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INT 15-60W November 2015. distinguishing molecules. Michael Pennington Jefferson Lab. q. q. q. q. q. 1. q ( i D - m ) q. - F F. =. q. 4. Q C D. q=u,d,s, c,b,t. q. q. g. g. q. q. q. q. q. q. q. g. g. q. q. q. q. q. q. q. q. q. q.
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INT 15-60W November 2015 distinguishing molecules Michael Pennington Jefferson Lab
q q q q q 1 q ( i D - m ) q - F F = q 4 QCD q=u,d,s, c,b,t
q q g g
q q q q q q q g g
q q q q q q q q q q q g g
q q q q q q q q q q q q g q g
q q q q q q q q q q q g g Can experiment distinguish between these configurations ?
q q q du c uc
K1B f2 ` ‘ f0 K0* K2* K1A h1 f0 j r a2 f2 a0 f0 f1 h3 a1 b1 w
Light Meson Spectrum negative parity ` h isoscalar isovector 0-+1-- 2-+ 3-- 0++ 1++ 1+- 2++ 4++ positiveparity 2.5 2.0 1.5 Mass (GeV) j 1.0 w r h 0.5 p 0 JPC
Light Meson Spectrum negative parity ` h isoscalar isovector 0-+1-- 2-+ 3-- 0++ 1++ 1+- 2++ 4++ positiveparity 2.5 2.0 1.5 Mass (GeV) j 1.0 w r h 0.5 p 0 JPC
Meson spectrum 3-- 2++ 4++ 2-- 1++ 3++ 1-- 2++ 0++ 2-+ 1+- 3+- L=3 1-- 0-+ L=2 L=1 s1 s2 q S = 0, 1 L=0 L q JPC radial
Meson spectrum K*0 K0 K*+ K+ f 1-- r+ + - r- 0-+ w r0 0 K*- K- K*0 K0 s1 s2 q S = 0, 1 L q 0-+ 1-- L=0
Vector decays p 3 p 2 energy 0 j K* w r p K
Vector decays p 3 p 2 f KK K* w r p K energy 0
Vector multiplet - - PC J = 1 s1 s2 q L S = 1, L = 0 q ds us ss ud du uu ± dd su sd
shifting of masses shifting of masses Vector multiplet Vector multiplet Vector multiplet + KK s
shifting of masses Vector multiplet + KK s
analyticity & complex energy plane resonance pole E Im E Re E
Hadroproduction R M(K) GeV M1 g p M2 exchange N B
Hadroproduction M1 g p M2 exchange N B
Hadroproduction M1 g p M2 exchange N B
Hadroproduction M1 g p M2 exchange N B
Hadroproduction M1 g p M2 exchange N B
Hadroproduction M1 g p M2 exchange N B
Hadroproduction M1 g p M2 exchange N B
Hadroproduction M1 g p M2 exchange N B
Hadroproduction M1 g p M2 exchange N B
Hadroproduction M1 g p M2 exchange N B
+ - (770)
Meson spectrum 3-- 2++ 4++ 2-- 1++ 3++ 1-- 2++ 0++ 2-+ 1+- 3+- L=3 1-- 0-+ L=2 L=1 s1 s2 q S = 0, 1 L=0 L q 0++ radial
Scalar mesons f (500) 0
Scalar mesons 1 1 GeV
Scalar multiplet s1 s2 q L q { 1 GeV k S = 1, L = 1
Scalar mesons I = J = 0 pp pp f (500) 1 1 0 0 0 0.4 0.4 0.8 0.8 1.2 1.2 1.6 1.6 M ()(GeV) M ()(GeV)
Hadron States Breit-Wigner 1 M2 – s - iMG E E x s = E2
p p p p M(pp) GeV r F(s,J) = 3 f1(s) cosJ s = M2 (pp) -1 0 cos J 1
Breit-Wigner 1 merely an approximation valid in the region of the pole M2 – s - iMG 1 M2 (s) – s x s = E2
Scalar mesons I = J = 0 pp pp f (500) 1 1 0 0 0 0.4 0.4 0.8 0.8 1.2 1.2 1.6 1.6 M ()(GeV) M ()(GeV)
Into the complex plane E Im E Re E ER= 441 -i 272 MeV Caprini, Colangelo, & Leutwyler
, KK f0 (980) 1 0 0.4 0.8 1.2 1.6 M ()(GeV) CERN-Munich, ANL, BNL
, KK f0 (980) 1 0 0.4 0.8 1.2 1.6 M ()(GeV) J/ (, KK) f0 (980) CERN-Munich, ANL, BNL BES
J/ (, KK) , KK f0 (980) 1 0 0.4 0.8 1.2 1.6 M ()(GeV) BES f0 (980) CERN-Munich, ANL, BNL
Scalar multiplet s1 s2 q L q { 1 GeV k S = 1, L = 1
diquarks: color tetraquark Jaffe & Wilczek Scalar diquarks [ud][us][ds] [cd][cu][cs]
Scalar meson multiplets qq qqqq n = u,d Jaffe