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CHARMED BOTTOM BARYON SPECTROSCOPY Zachary S. Brown, William Detmold, Stefan Meinel, Konstantinos Orginos 1 Thursday, August 1, 2013

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Page 1: CHARMED BOTTOM BARYON SPECTROSCOPY - uni-mainz.de · LANDSCAPE • Significant experimental progress in recent years Many singly heavy baryon observations • Productive period for

CHARMED BOTTOM BARYON SPECTROSCOPY

Zachary S. Brown, William Detmold, Stefan Meinel, Konstantinos Orginos

1

Thursday, August 1, 2013

Page 2: CHARMED BOTTOM BARYON SPECTROSCOPY - uni-mainz.de · LANDSCAPE • Significant experimental progress in recent years Many singly heavy baryon observations • Productive period for

OUTLINE

• Landscape of heavy baryon spectroscopy

•Details of our calculation

• Extrapolations

• Results2

Thursday, August 1, 2013

Page 3: CHARMED BOTTOM BARYON SPECTROSCOPY - uni-mainz.de · LANDSCAPE • Significant experimental progress in recent years Many singly heavy baryon observations • Productive period for

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

Thursday, August 1, 2013

Page 4: CHARMED BOTTOM BARYON SPECTROSCOPY - uni-mainz.de · LANDSCAPE • Significant experimental progress in recent years Many singly heavy baryon observations • Productive period for

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

Thursday, August 1, 2013

Page 5: CHARMED BOTTOM BARYON SPECTROSCOPY - uni-mainz.de · LANDSCAPE • Significant experimental progress in recent years Many singly heavy baryon observations • Productive period for

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

Thursday, August 1, 2013

Page 6: CHARMED BOTTOM BARYON SPECTROSCOPY - uni-mainz.de · LANDSCAPE • Significant experimental progress in recent years Many singly heavy baryon observations • Productive period for

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

Thursday, August 1, 2013

Page 7: CHARMED BOTTOM BARYON SPECTROSCOPY - uni-mainz.de · LANDSCAPE • Significant experimental progress in recent years Many singly heavy baryon observations • Productive period for

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

* * *

Thursday, August 1, 2013

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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

* * *

Thursday, August 1, 2013

Page 9: CHARMED BOTTOM BARYON SPECTROSCOPY - uni-mainz.de · LANDSCAPE • Significant experimental progress in recent years Many singly heavy baryon observations • Productive period for

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

Thursday, August 1, 2013

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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

Thursday, August 1, 2013

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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

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∗

= M0 +

−(1/2)(1/4)

∆H − f2σ

2m2

πvv− f2σm2

πss+ g21

M (3/2)

ΞQQ

M (3/2)Ξ∗

QQ

.

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

Thursday, August 1, 2013

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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

Thursday, August 1, 2013

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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

Thursday, August 1, 2013

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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) -

Thursday, August 1, 2013

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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)

Thursday, August 1, 2013

Page 16: CHARMED BOTTOM BARYON SPECTROSCOPY - uni-mainz.de · LANDSCAPE • Significant experimental progress in recent years Many singly heavy baryon observations • Productive period for

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

Thursday, August 1, 2013

Page 17: CHARMED BOTTOM BARYON SPECTROSCOPY - uni-mainz.de · LANDSCAPE • Significant experimental progress in recent years Many singly heavy baryon observations • Productive period for

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.

Thursday, August 1, 2013

Page 18: CHARMED BOTTOM BARYON SPECTROSCOPY - uni-mainz.de · LANDSCAPE • Significant experimental progress in recent years Many singly heavy baryon observations • Productive period for

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.

Thursday, August 1, 2013

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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)

Thursday, August 1, 2013

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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

Thursday, August 1, 2013

Page 21: CHARMED BOTTOM BARYON SPECTROSCOPY - uni-mainz.de · LANDSCAPE • Significant experimental progress in recent years Many singly heavy baryon observations • Productive period for

• 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.

Thursday, August 1, 2013