Cascade Baryon Spectrum from Lattice QCD Nilmani Mathur Tata Institute, India.
-
Upload
domenic-bond -
Category
Documents
-
view
218 -
download
0
description
Transcript of Cascade Baryon Spectrum from Lattice QCD Nilmani Mathur Tata Institute, India.
![Page 1: Cascade Baryon Spectrum from Lattice QCD Nilmani Mathur Tata Institute, India.](https://reader034.fdocuments.in/reader034/viewer/2022051305/5a4d1b767f8b9ab0599b72b2/html5/thumbnails/1.jpg)
Cascade Baryon Spectrumfrom Lattice QCD
Nilmani MathurTata Institute, India
![Page 2: Cascade Baryon Spectrum from Lattice QCD Nilmani Mathur Tata Institute, India.](https://reader034.fdocuments.in/reader034/viewer/2022051305/5a4d1b767f8b9ab0599b72b2/html5/thumbnails/2.jpg)
Collaborators
• J. Dudek, R. G. Edwards, H. -W. Lin. B. Joo, D. Richards (JLab)
• A. Lichtl (BNL)• J. Bulava, C. Morningstar, J. Foley (CMU)• E. Engelson, S. Wallace (UM)• G. Fleming (Yale)• K. Juge (PU)
![Page 3: Cascade Baryon Spectrum from Lattice QCD Nilmani Mathur Tata Institute, India.](https://reader034.fdocuments.in/reader034/viewer/2022051305/5a4d1b767f8b9ab0599b72b2/html5/thumbnails/3.jpg)
…PDG Live
(1314)
(1321)
![Page 4: Cascade Baryon Spectrum from Lattice QCD Nilmani Mathur Tata Institute, India.](https://reader034.fdocuments.in/reader034/viewer/2022051305/5a4d1b767f8b9ab0599b72b2/html5/thumbnails/4.jpg)
…PDG Live
![Page 5: Cascade Baryon Spectrum from Lattice QCD Nilmani Mathur Tata Institute, India.](https://reader034.fdocuments.in/reader034/viewer/2022051305/5a4d1b767f8b9ab0599b72b2/html5/thumbnails/5.jpg)
…V. Zielgler (GlueX meeting)
![Page 6: Cascade Baryon Spectrum from Lattice QCD Nilmani Mathur Tata Institute, India.](https://reader034.fdocuments.in/reader034/viewer/2022051305/5a4d1b767f8b9ab0599b72b2/html5/thumbnails/6.jpg)
Why Cascades?
Except for ground state 1/2+, 3/2+, 3/2-, masses and quantum numbers for other cascade states are not known. Even ground state 1/2- is not known (Ξ(1690)?)
Narrow width reduces potential overlap with neighboring states
Cascades states will be searched in various experiments (e.g., GlueX)
Lattice calculations can predict QCD allowed states before experiments find physical states.
Due to presence of two strange quarks chiral extrapolation will be easier.
![Page 7: Cascade Baryon Spectrum from Lattice QCD Nilmani Mathur Tata Institute, India.](https://reader034.fdocuments.in/reader034/viewer/2022051305/5a4d1b767f8b9ab0599b72b2/html5/thumbnails/7.jpg)
Octahedral group and lattice operators
Λ J
G1
G2
H
1/2⊕7/2⊕9/2⊕11/2 …5/2⊕7/2⊕11/2⊕13/2 …3/2⊕5/2⊕7/2⊕9/2 …
Λ J
A1
A2
E
T1
T2
0⊕4⊕6⊕8 …3⊕6⊕7⊕9 …2⊕4⊕5⊕6 …1⊕3⊕4⊕5 …2⊕3⊕4⊕5 …
BaryonBaryon
MesonMeson
……R.C. Johnson, Phys. Lett.B 113, 147(1982)R.C. Johnson, Phys. Lett.B 113, 147(1982)
![Page 8: Cascade Baryon Spectrum from Lattice QCD Nilmani Mathur Tata Institute, India.](https://reader034.fdocuments.in/reader034/viewer/2022051305/5a4d1b767f8b9ab0599b72b2/html5/thumbnails/8.jpg)
Radial structure : displacements of different lengthsRadial structure : displacements of different lengthsOrbital structure : displacements in different directionsOrbital structure : displacements in different directions
……C. MorningstarC. Morningstar
![Page 9: Cascade Baryon Spectrum from Lattice QCD Nilmani Mathur Tata Institute, India.](https://reader034.fdocuments.in/reader034/viewer/2022051305/5a4d1b767f8b9ab0599b72b2/html5/thumbnails/9.jpg)
Lattice operator construction
• Construct operator which transform irreducibly under the symmetries of the lattice
• Classify operators according to the irreps of Oh :
G1g, G1u, G1g, G1u,Hg, Hu
• Basic building blocks : smeared, coariant displaced quark fields
• Construct translationaly invariant elemental operators
• Flavor structure isospin, color structure gauge invariance
• Group theoretical projections onto irreps of Oh :
)210(nt displaceme link :)(~~ )( ..,, j nxDAa
nj
CcnkBb
njAa
niabc
FABC
F xDxDxDxB )(~~)(~~)(~~)(
RFiR
OROi UtBURD
gd
tBDh
Dh
F
)()()(
PRD 72,094506 (2005) PRD 72,094506 (2005) A. Lichtl thesis, A. Lichtl thesis, hep-lat/0609019hep-lat/0609019
![Page 10: Cascade Baryon Spectrum from Lattice QCD Nilmani Mathur Tata Institute, India.](https://reader034.fdocuments.in/reader034/viewer/2022051305/5a4d1b767f8b9ab0599b72b2/html5/thumbnails/10.jpg)
G1 Total operators : 270• Single site : 4
• Singly displaced : 38
• Doubly displaced-I : 36
• Doubly displaced-L : 96
• Triply displaced T : 96
![Page 11: Cascade Baryon Spectrum from Lattice QCD Nilmani Mathur Tata Institute, India.](https://reader034.fdocuments.in/reader034/viewer/2022051305/5a4d1b767f8b9ab0599b72b2/html5/thumbnails/11.jpg)
G2 Total operators : 218• Single site : 0
• Singly displaced : 14
• Doubly displaced-I : 12
• Doubly displaced-L : 96
• Triply displaced T : 96
![Page 12: Cascade Baryon Spectrum from Lattice QCD Nilmani Mathur Tata Institute, India.](https://reader034.fdocuments.in/reader034/viewer/2022051305/5a4d1b767f8b9ab0599b72b2/html5/thumbnails/12.jpg)
H Total operators : 487• Single site : 3
• Singly displaced : 52
• Doubly displaced-I : 48
• Doubly displaced-L : 192
• Triply displaced T : 192
![Page 13: Cascade Baryon Spectrum from Lattice QCD Nilmani Mathur Tata Institute, India.](https://reader034.fdocuments.in/reader034/viewer/2022051305/5a4d1b767f8b9ab0599b72b2/html5/thumbnails/13.jpg)
• Nf = 2, anisotropic clover lattice– at ~ 5.556 GeV(-1)– Lattice size : 243 X 64– # Configurations : 860
• Quenched anisotropic clover lattice (not analyzed yet)– at = 6.1 GeV(-1)– Lattice size : 163 X 64
• Nf = 2+1, anisotropic clover lattices (cascade calculation will be started soon)
![Page 14: Cascade Baryon Spectrum from Lattice QCD Nilmani Mathur Tata Institute, India.](https://reader034.fdocuments.in/reader034/viewer/2022051305/5a4d1b767f8b9ab0599b72b2/html5/thumbnails/14.jpg)
Ground state spectrum (Nf=2)
![Page 15: Cascade Baryon Spectrum from Lattice QCD Nilmani Mathur Tata Institute, India.](https://reader034.fdocuments.in/reader034/viewer/2022051305/5a4d1b767f8b9ab0599b72b2/html5/thumbnails/15.jpg)
Pruning
• All operators do not overlap equally and it will be very difficult to use all of them.
• Need pruning to choose a good operator set for each representation.
• Error in diagonal effective masses.• Construct average correlator matrix in each
representation and find condition number.• Find a matrix with minimum condition
number for each representation.
![Page 16: Cascade Baryon Spectrum from Lattice QCD Nilmani Mathur Tata Institute, India.](https://reader034.fdocuments.in/reader034/viewer/2022051305/5a4d1b767f8b9ab0599b72b2/html5/thumbnails/16.jpg)
![Page 17: Cascade Baryon Spectrum from Lattice QCD Nilmani Mathur Tata Institute, India.](https://reader034.fdocuments.in/reader034/viewer/2022051305/5a4d1b767f8b9ab0599b72b2/html5/thumbnails/17.jpg)
![Page 18: Cascade Baryon Spectrum from Lattice QCD Nilmani Mathur Tata Institute, India.](https://reader034.fdocuments.in/reader034/viewer/2022051305/5a4d1b767f8b9ab0599b72b2/html5/thumbnails/18.jpg)
Effective masses for different channels
![Page 19: Cascade Baryon Spectrum from Lattice QCD Nilmani Mathur Tata Institute, India.](https://reader034.fdocuments.in/reader034/viewer/2022051305/5a4d1b767f8b9ab0599b72b2/html5/thumbnails/19.jpg)
Effective masses for positive parity channels
![Page 20: Cascade Baryon Spectrum from Lattice QCD Nilmani Mathur Tata Institute, India.](https://reader034.fdocuments.in/reader034/viewer/2022051305/5a4d1b767f8b9ab0599b72b2/html5/thumbnails/20.jpg)
Effective masses for negative parity channels
![Page 21: Cascade Baryon Spectrum from Lattice QCD Nilmani Mathur Tata Institute, India.](https://reader034.fdocuments.in/reader034/viewer/2022051305/5a4d1b767f8b9ab0599b72b2/html5/thumbnails/21.jpg)
Effective masses for G1(1/2) channel
![Page 22: Cascade Baryon Spectrum from Lattice QCD Nilmani Mathur Tata Institute, India.](https://reader034.fdocuments.in/reader034/viewer/2022051305/5a4d1b767f8b9ab0599b72b2/html5/thumbnails/22.jpg)
Effective masses for G1(1/2) channel
![Page 23: Cascade Baryon Spectrum from Lattice QCD Nilmani Mathur Tata Institute, India.](https://reader034.fdocuments.in/reader034/viewer/2022051305/5a4d1b767f8b9ab0599b72b2/html5/thumbnails/23.jpg)
Comparison between G1u and regular effective masses
![Page 24: Cascade Baryon Spectrum from Lattice QCD Nilmani Mathur Tata Institute, India.](https://reader034.fdocuments.in/reader034/viewer/2022051305/5a4d1b767f8b9ab0599b72b2/html5/thumbnails/24.jpg)
Effective masses for G2 channel
![Page 25: Cascade Baryon Spectrum from Lattice QCD Nilmani Mathur Tata Institute, India.](https://reader034.fdocuments.in/reader034/viewer/2022051305/5a4d1b767f8b9ab0599b72b2/html5/thumbnails/25.jpg)
Effective masses for H channel
![Page 26: Cascade Baryon Spectrum from Lattice QCD Nilmani Mathur Tata Institute, India.](https://reader034.fdocuments.in/reader034/viewer/2022051305/5a4d1b767f8b9ab0599b72b2/html5/thumbnails/26.jpg)
Effective masses for H channel
![Page 27: Cascade Baryon Spectrum from Lattice QCD Nilmani Mathur Tata Institute, India.](https://reader034.fdocuments.in/reader034/viewer/2022051305/5a4d1b767f8b9ab0599b72b2/html5/thumbnails/27.jpg)
![Page 28: Cascade Baryon Spectrum from Lattice QCD Nilmani Mathur Tata Institute, India.](https://reader034.fdocuments.in/reader034/viewer/2022051305/5a4d1b767f8b9ab0599b72b2/html5/thumbnails/28.jpg)
Conclusion
Lattice QCD can predict the masses and other quantum numbers of cascade states before experiments (e.g, CLAS12 and GLUEX) can tell us about those.
First result by using group theoretical operators is quite encouraging.
This calculation will be repeated on anisotropic 2+1 clover lattices at various volumes and lattice spacings.