Download presentation

Presentation is loading. Please wait.

Published byAlexis Bird Modified over 4 years ago

1
Lattice Perturbation Theory from Monte Carlo Simulation Kit Yan Wong (Glasgow University) H. Trottier (Simon Fraser University) R. Woloshyn (TRIUMF) C. Davies (Glasgow University)

2
Motivation: we need perturbation theory example 1. determination of [Q. Mason et al., PRL95, 052002 (2005)] 1/15 0.1150.1170.119 world average: 0.1187 0.002 convert to measure this in simulation solve for need c 1, c 2, …

3
example 2. quark masses [Q. Mason et al., hep-ph/0511160] [M. Nobes & H. Trottier, hep-lat/0509128] 2/15 (MeV) lattice PDG need connection between bare mass and MS mass Motivation: we need perturbation theory

4
Lattice PT is Difficult! some of the 2-loop diagrams in the expansion for a Wilson loop: taken from Q. Masons Ph.D Thesis (Cornell Electronic Library) 3/15 particularly true for highly improved actions and higher-order calculations

5
so … we need another method Monte Carlo Simulations at Weak Couplings 4/15

6
Weak Coupling Simulations 1. do several simulations at weak couplings weak couplings perturbative phase weak couplings? ~ 9.5-80.0 ( s ~ 0.1-0.01) 2. fit the data points with an expansion in s 5/15

7
Weak Coupling Simulations example c 1 : intercept c 2 : slope c 3 : curvature 1. 9 simulations at weak couplings 9 data points ( V,-lnW R,T ) 2. fit the points to 6/15 W 2,2

8
Weak Coupling Simulations many calculations have been done before: Dimm, Lepage & Mackenzie [Nucl. Phys. B (Proc. Suppl.), 42, 403 (1995)] 1 st -order mass renormalization for Wilson fermions Trottier, Shakespeare, Lepage & Mackenzie [PRD, 65, 094502 (2002)] 3 rd -order Wilson loops for the Wilson plaquette action Hart, Horgan & Storoni [PRD, 70, 034501 (2004)] tadpole factor in pure gauge theories quenched calculations here: unquenched (MILC) important cross-check of the 2-loop expansions used in the s calculation 7/15

9
Difficulties need very accurate measurements: statistical errors ~ 10 -5 – 10 -6 ~ s 3 why? want to probe the 3 rd -order coefficients challenge: tight control of systematic errors, both in simulations and analysis tunneling between Z 3 center phases fitting and truncation errors zero momentum modes step size errors in simulation equations autocorrelation inaccuracy in matrix inversions 8/15

10
Simulation Parameters MILC action, 9 couplings 0 9.50.08380.1278 11.00.07230.1016 13.50.05890.0741 16.00.04970.0619 19.00.04190.0506 24.00.03320.0382 32.00.02490.0271 47.00.01690.0183 80.00.00990.0101 input from analytic PT 0 9/15 (not necessary) use 2-loop expansion of the plaquette

11
Results 0.88(26)-0.599(19)1.2342(4)0.85(16)-0.595(3)1.2341(0)2x3 0.58(20)-0.641(15)1.1499(4)0.59(9)-0.643(2)1.1499(0)2x2 0.37(19)-0.599(14)0.9845(3)0.38(6)-0.595(1)0.9845(0)1x3 0.20(18)-0.644(13)0.9251(3)0.23(5)-0.646(9)0.9252(0)1x2 c3c3 c2c2 c1c1 c3c3 c2c2 c1c1 Loop Perturbation TheoryMonte Carlo Simulation 0.82(15)-0.594(7)2x3 0.59(14)-0.642(7)2x2 0.39(13)-0.600(6)1x3 0.26(12)-0.649(5)1x2 c3c3 c2c2 Loop Fit with c 1 fixed to PT values 0.84(8)2x3 0.61(6)2x2 0.28(5)1x3 0.21(4)1x2 c3c3 Loop Both c 1, c 2 fixed 10/15

12
Results – 2x2 Loop k1k1 k3k3 k2k2 k 1 = k 3 = k 2 = 11/15

13
provides an important cross-check of the 2-loop expansions used in the s calculation 12/15

14
Results – NRQCD NRQCD action: ; dispersion relation c 1 : intercept c 2 : slope c 3 : curvature aM 0 = 8.0 zero energymass renormalization zero energy: mass renormalization: c 1 : intercept c 2 : slope c 3 : curvature 13/15

15
Results – NRQCD zero energymass renormalization 2.773(7)2.7824.0 2.648(5)2.6555.0 2.565(5)2.5706.0 2.447(2)2.4508.0 MCPT M0aM0a 0.798(10)0.7704.0 0.842(9)0.8205.0 0.849(7)0.8306.0 0.867(6)0.8508.0 MCPT M0aM0a c1:c1: Predictions for c 2 and c 3 : 7.4(1.4)-2.13(7)4.0 7.3(1.4)-2.02(7)5.0 6.3(1.4)-1.91(7)6.0 5.9(1.4)-1.98(8)8.0 c3c3 c2c2 M0aM0a -0.28(6.7)-0.91(56)4.0 0.7(6.1)-0.53(45)5.0 0.5(5.3)-0.33(42)6.0 -0.2(4.9)-0.34(37)8.0 c3c3 c2c2 M0aM0a 14/15

16
Conclusions 1. numerical approach is simple; give accurate results 2. Wilson loops: impressive agreement important for the s calculation 3. in progress: HIST, mNRQCD 15/15

Similar presentations

Presentation is loading. Please wait....

OK

Resistência dos Materiais, 5ª ed.

Resistência dos Materiais, 5ª ed.

© 2018 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google