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CHARMED BOTTOM BARYON SPECTROSCOPY
Zachary S. Brown, William Detmold, Stefan Meinel, Konstantinos Orginos
1
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OUTLINE
• Landscape of heavy baryon spectroscopy
•Details of our calculation
• Extrapolations
• Results2
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LANDSCAPE
• Significant experimental progress in recent yearsMany singly heavy baryon observations
• Productive period for LQCD spectroscopy of heavy baryons
3from H.W. Lin [1] (extended to present)
Group Nf SH a−1
t (GeV) L (fm)Bowler et al. 0 tree clover 2.9 1.63Lewis et al. 0 D234 1.8, 2.2, 2.6 1.97Mathur et al. 0 NRQCD 1.8, 2.2 2.64, 2.1Flynn et al. 0 NP clover 2.6 1.82Chiu et al. 0 ODWF 2.23 1.77Na et al. 2 + 1 Fermilab 2.2, 1.6, 1.3 2.5Liu et al. 2 + 1 RHQ 1.6 2.5
Briceno et al. 2 + 1 + 1 RHQ 1.6, 2.2, 3.4 2.7 - 4.1Alexandrou et al. 2 Osterwalder-Seiler 3.5, 2.8, 2.2 1.8 - 2.74Namekawa et al. 2 + 1 RHQ 2.2 2.9
CONTROVERSYΩb,Ξcc
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LANDSCAPE
4
Splitting(Stat)(Extrap)(Scale) Experiment
Bs −Bd 71.2(2.2)(1.2)(4.2) 87.1(0.6)Λb −Bd 340(11)(8.1)(24) 341.0(1.6)Ξb −Bd 484.7(7.7)(6.2)(32) 513(3)Σb −Bd 615(15)(12)(40) 554(3)Ξb −Bd 672(10)(9.1)(44) –
Ωb −Bd 749.2(9.8)(9.0)(49) 786(7)/886(16)Λb −Bs 261(10)(8.5)(19) 253.9(1.7)Ξb − Λb 157.2(5.2)(3.4)(9.0) 172(3)Σb − Λb 274(13)(13)(17) 213(3)Ξb − Λb 335(15)(10)(20) –
Ωb − Λb 414(12)(9.5)(25) 445(7)/545(16)Ξb − Σb 62.6(2.6)(2.0)(3.9) –
Ωb − Ξb 81.5(2.7)(3.4)(4.9) –
from H.W. Lin [1] (not current)
• Test agreement between lattice/expt. and lattice/lattice
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LANDSCAPE
5
Liu et al. directLiu et al. splittingNa et al. a0.12 fmFlynn et al.Mathur et al.Chiu et al.
c c c c c cc cc2.0
2.5
3.0
3.5
4.0
GeV
from PDG [2]
• Test agreement between lattice/expt. and lattice/lattice
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LANDSCAPE
6
LQCD
QM
RTQM
RQM
FHT
HQET
3300 3400 3500 3600 3700 3800Mcc MeV
LQCD
1!Nc
HQET
RQM
FHT
5850 5900 5950 6000 6050 6100 6150 6200M!b ""MeV#
from H.W. Lin [2] and Refs. therein
• Test agreement between lattice/models
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GOAL OF OUR CALCULATION:
7
• Comprehensive calculation of the low lying heavy baryon spectrumInclude all states with charmed and bottom quarks.
2
4
6
8
10
12
14
16
Mas
s (G
eV)
Charmed Bottom Hadron Spectrum
* * *
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GOAL OF OUR CALCULATION:
8
• Comprehensive calculation of the low lying heavy baryon spectrumInclude all states with charmed and bottom quarks.
• Include mixed charmed bottom baryons
2
4
6
8
10
12
14
16
Mas
s (G
eV)
Charmed Bottom Hadron Spectrum
* * *
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DETAILS OF THE CALCULATION
• Use ensembles generated by RBC/UKQCD collaboration [3] Iwasaki gauge action 2+1 flavors of dynamical DWF with Mass ranges:
• Relativistic heavy quark action [4] for charmed quarks Non-perturbatively tune and Use tree level values for and
• NRQCD for bottom accurate through order One loop improved calculated by Tom Hammant [5]
9
L5 = 16
ν m0
cE cB
c4
a ∼ 0.0849, 0.1119 fm
v4
L ∼ 2.7fm
mvvπ = (227− 352)MeV, mss
π = (295− 352)MeV
mvvK = (523− 586)MeV
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• Use baryon operators of the form:
• Use different smearing to construct operator basis:
• Simultaneous matrix fits, optimized ranges:
INTERPOLATING OPERATORS AND FITTING METHODOLOGY: BARYON OPS
10
O5[q, q, q
]α = abc (Cγ5)βγ qaβ q
bγ (P+q
)cα,
Oj [q, q, q
]α = abc (Cγj)βγ qaβ q
bγ (P+q
)cα,
2 x 4 for qqQ, qQQ2 x 2 for QQQ
1.90
1.95
2.00
2.05
2.10
aEeff
O[c, c, b]O[c, c, b]
1.90
1.95
2.00
2.05
2.10
aEeff
O[c, c, b]O[c, c, b]
1.90
1.95
2.00
2.05
2.10
aEeff
O[c, c, b]O[c, c, b]
0 5 10 15 20
t/a
1.90
1.95
2.00
2.05
2.10
aEeff
O[c, c, b]O[c, c, b]
1.90
1.95
2.00
2.05
2.10
aEeff
O[c, c, b]O[c, c, b]
1.90
1.95
2.00
2.05
2.10
aEeff
O[c, c, b]O[c, c, b]
1.90
1.95
2.00
2.05
2.10
aEeff
O[c, c, b]O[c, c, b]
0 5 10 15 20
t/a
1.90
1.95
2.00
2.05
2.10
aEeff
O[c, c, b]O[c, c, b]
χ2/d.o.f. = 1.4 χ2/d.o.f. = 0.94
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CHIRAL / CONTINUUM EXTRAPOLATIONS
• Tiburzi [6] for singly heavy (coupled fits, SU(2), extended to ):
•Mathur et. al [7] for doubly heavy (coupled fits, SU(2)):
• Assume chiral dependence to be negligible for triply heavy:
11
MΛ
MΣ
MΣ∗
= M0 +
0
∆Σ,Λ
∆Σ∗,Λ
+f2
8
λ32
λ1
λ1
m2πvv
+f2
4
λ4
λ2
λ2
m2πss
+ g23
M (3/2)
g3,Λ
M (3/2)g3,Σ
M (3/2)g3,Σ∗
+ g22
0
M (3/2)g2,Σ
M (3/2)g2,Σ∗
MΞ
MΞ∗
= M0 +
−(1/2)(1/4)
∆H − f2σ
2m2
πvv− f2σm2
πss+ g21
M (3/2)
ΞQQ
M (3/2)Ξ∗
.
MΩ(∗)
QQQ= M0 + caa
2
O (1/mQ)
MB = M0(µ) +∆B(µ) +M (B)1 (µ) +M (B)
3/2 (µ)
FV corrections from Detmold et al. [8], g widths from Detmold et al. [9]
+Oa2
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CHIRAL / CONTINUUM EXTRAPOLATIONS
12
2.0
2.1
2.2
2.3
2.4
2.5
2.6
m(G
eV)
Λc
2.2
2.3
2.4
2.5
2.6
2.7
2.8
m(G
eV)
Σc
0.02 0.04 0.06 0.08 0.10 0.12 0.14
m2π (GeV2)
2.2
2.3
2.4
2.5
2.6
2.7
2.8
m(G
eV)
Σ∗c
2.1
2.2
2.3
2.4
2.5
2.6
2.7
m(G
eV)
Ξc
2.3
2.4
2.5
2.6
2.7
2.8
2.9
m(G
eV)
Ξc
0.02 0.04 0.06 0.08 0.10 0.12 0.14
m2π (GeV2)
2.3
2.4
2.5
2.6
2.7
2.8
2.9m
(GeV
)
Ξ∗c
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CHIRAL / CONTINUUM EXTRAPOLATIONS
13
5.5
5.6
5.7
5.8
5.9
6.0
m(G
eV)
Ξb
5.7
5.8
5.9
6.0
6.1
6.2
m(G
eV)
Ξb
0.02 0.04 0.06 0.08 0.10 0.12 0.14
m2π (GeV2)
5.7
5.8
5.9
6.0
6.1
6.2
m(G
eV)
Ξ∗b
5.2
5.4
5.6
5.8
6.0
m(G
eV)
Λb
5.4
5.6
5.8
6.0
6.2
m(G
eV)
Σb
0.02 0.04 0.06 0.08 0.10 0.12 0.14
m2π (GeV2)
5.4
5.6
5.8
6.0
6.2m
(GeV
)
Σ∗b
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CHIRAL / CONTINUUM EXTRAPOLATIONS:RESULTS
14
Baryon Lattice (GeV) Expt. (GeV) Baryon Lattice (GeV) Expt. (GeV)
Λc 2.137(74) 2.286 Λb 5.456(114) 5.619Σc 2.444(81) 2.454 Σb 5.781(96) 5.811Σ∗
c 2.518(82) 2.518 Σ∗b 5.802(97) 5.832
Ξc 2.372(58) 2.467 Ξb 5.760(80) 5.791Ξc 2.526(62) 2.575 Ξ
b 5.947(81) -Ξ∗c 2.600(62) 2.645 Ξ∗
b 5.971(81) -Ωc 2.615(67) 2.685 Ωb 6.008(80) 6.071Ω∗
c 2.690(67) 2.765 Ω∗b 6.036(80) -
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CHIRAL / CONTINUUM EXTRAPOLATIONS:RESULTS
15
Baryon Lattice (GeV) Baryon Lattice (GeV) Baryon Lattice (GeV)
Ξcc 3.558(39) Ξcb 6.877(52) Ξbb 10.185(53)Ξ∗cc 3.627(54) Ξ∗
cb 6.915(62) Ξ∗bb 10.191(56)
Ωcc 3.689(38) Ωcb 6.973(48) Ωbb 10.250(51)Ω∗
cc 3.773(38) Ω∗cb 7.040(48) Ω∗
bb 10.283(51)Ωccc 4.794(9) Ωccb 7.989(11) Ω∗
ccb 8.012(12)Ωcbb 11.177(9) Ω∗
cbb 11.206(11) Ωbbb 14.370(10)
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CONSIDERATION OF UNCERTAINTIES
• All statistical uncertainties
• Systematics may enter through several sources:
•Optimization routine for extracting masses
• Absence of NNLO correction terms to chiral extrapolations
• Currently being explored... but how do our results compare?
16
M = M0 +Om4
πvv
+O
m4
πvs
+O
m2
πvvm2
πvs
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RESULTS: CHARM COMPARISONS
17
2
2.2
2.4
2.6
2.8
3
GeV
c c c*
c c’
c*
c c*
Briceno et al.Namekawa et al.Alexandrou et al.Liu et al.Na et al.Brown et al.
3
3.5
4
4.5
5
GeV
cc*cc cc
*cc ccc
Briceno et al.Namekawa et al.Alexandrou et al.Liu et al.Na et al.Brown et al.
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RESULTS: BOTTOM COMPARISONS
18
5.3
5.5
5.7
5.9
6.1
6.3
GeV
b b b*
b b’
b*
b b*
Lewis et al.Brown et al.Lin et al.Na et al.Detmold et al.
10
10.1
10.2
10.3
10.4
10.5
bb bb*
bb bb*
GeV
Lewis et al.Brown et al.Na et al.
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6.6
6.8
7
7.2
7.4
7.6
7.8
cb cb*
cb cb*
GeV
Roberts et al. (QM)Martynenko et al. (RTQM)Ebert et al. (RQM)Roncaglia et al. (FH)Mathur et al. (lattice)Brown et al. (lattice)
RESULTS: MIXED COMPARISONS
19
4
6
8
10
12
14
16
ccc ccb ccb*
cbb cbb*
bbb
GeV
Roberts et al. (QM)Martynenko et al. (RTQM)Brown et al. (lattice)
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FUTURE OUTLOOK
• Still need to nail down systematic uncertainties
• Possible repetition of calculation with larger operator basis and relativistic bottom quarks?
20
THANK YOU
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• References:
[1] J. Beringer et al. (Particle Data Group), Phys. Rev. D86, 010001 (2012)
[2] H. W. Lin, Chin. J. Phys. 49 (2011) 827 [arXiv:1106.1608 [hep-lat]]
[3] Y. Aoki et al., “Continuum Limit Physics from 2+1 Flavor Domain Wall QCD,” Phys.Rev., vol. D83, p. 074508, 2011.
[4] A. X. El-Khadra, A. S. Kronfeld, and P. B. Mackenzie, Phys. Rev. D55, 3933 (1997), hep-lat/9604004
[5] T. C. Hammant, A. G. Hart, G. M. von Hippel, R. R. Horgan and C. J. Monahan, Phys. Rev. Lett. 107, 112002 (2011) [arXiv:1105.5309 [hep-lat]]
[6]B. C. Tiburzi, “Baryon masses in partially quenched heavy hadron chiral perturbation theory,” Phys.Rev., vol. D71, p. 034501, 2005.
[7]T. Mehen and B. C. Tiburzi, “Doubly heavy baryons and quark-diquark symmetry in quenched and partially quenched chiral perturbation theory,” Phys.Rev., vol. D74, p. 054505, 2006.
[8] W. Detmold, C.-J. D. Lin, and S. Meinel, “Axial couplings in heavy hadron chiral perturbation theory at the next-to-leading order,” Phys.Rev., vol. D84, p. 094502, 2011.
[9] W. Detmold, C.-J. D. Lin, and S. Meinel, “Axial couplings and strong decay widths of heavy hadrons,” Phys.Rev.Lett., vol. 108, p. 172003, 2012.
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