1. Probing TeV scale physics in precision UCN decays Rajan Gupta Theoretical Division Los Alamos National Lab Lattice 2013 Mainz, 30 July 2013 Superconducting Spectrometer Neutron Polarizing/Spin-flipper Magnet 1 LAUR-12-20208 Theory and Experimental effort centered at LANL

2. Tanmoy Bhattacharya (LANL) Vincenzo Cirigliano (LANL) Saul Cohen (U of Washington) Alberto Filipuzzi (Valencia, Spain) Martin Gonzalez-Alonso (Madison, Wisconsin) Michael Graesser (LANL) Rajan Gupta (LANL) Anosh Joseph (LANL) Huey-Wen Lin (U of Washington) Theory and Lattice QCD Collaboration (PNDME) 2 PRD85:5 (2012) 054512 arXiv:1110.6448 arXiv:1306.5435

3. Precision calculations of g S, g T using Lattice QCD g T ~ g S ~ 3 Goal: 10-20% accuracy X BSM T. Bhattacharya, S. Cohen, R. Gupta, H-W Lin, A. Joseph

4. Impact of reducing errors in g S and g T from 50→10% 4 |B 1 -b| < 10 -3 |b| < 10 -3 b 0+ = 2.6 (4.3) ∗ 10 -3 Allowed region in [ ε S, ε T ] (90% contours) g T ~ g S ~ Expt. input Limited by precision of ME

5. Achieving 10-20% uncertainty is a realistic goal but requires: –High Statistics: computer resources from USQCD, XSEDE, LANL –Controlling all Systematic Errors: Finite volume effects Contamination from excited states Chiral Extrapolations to physical u and d quark masses →Extrapolation to the continuum limit (lattice spacing a → 0) Non-perturbative renormalization of bilinears using the RI smom scheme n p × n p × n p × Lattice QCD calculation of OiqOiq n p × Isolate the neutron e -M n τ Project on the proton e -M p τ u d u u dd 5

6. Lattice setup: Choices we made Gauge configurations with 2+1+1 flavor of dynamical quarks –HISQ lattices generated by the MILC collaboration (short-term) Analysis using clover fermions (Clover on HISQ) –Issue of exceptional Configurations – extensive tests Improving Signal in Baryon Correlators –Large smearing of source used in matrix inversion (p = 0) –HYP smearing of gauge configurations Study multiple time separations between the source (neutron) and sink (proton) to study & reduce excited state contribution 6 np × t sep

7. Sequential propagators with nucleon insertion at p=0 7 p p u d u O(p,t) Initial inversion of Dirac operator with smeared source Sequential inversion with (n,p) insertion at p=0

8. 2+1+1 flavor HISQ lattices: goal 1000 configs m s set to its physical value using M ss 8 a(fm)m l /m s Lattice Volume M π LM π (MeV)Configs. Analyzed 0.120.224 3 × 644.543051013/1013 0.120.132 3 × 644.29217958/958 0.090.232 3 × 964.5313881/1000 0.090.148 3 × 964.73220890/1000 0.060.248 3 × 1444.53320800/1000 0.060.164 3 × 1444.282290/1000

9. Issues in Analysis 9

10. Signal in 2-point baryon correlators a = 0.12 fm lattices with M π = 310 MeV (Total of 1013 Configurations, each with 4 sources) 10 SS: Effective Mass Plot M eff 507 Conf 506 Conf 1013 conf

11. 2-point function → M N 11

12. Findings at a=0.12 fm with M π =310, 220 MeV Statistical analysis of ~1000 configurations and as 2 subsets of ~500 configurations – All three estimates consistent within 1–2 σ – Errors of the 2 subsets ~√2 larger than the full set – Variation in g Γ between 2 subsets ≈ Δt dependence – Signal improves as a → 0 12 Need > 4x1000 configurations before t sep dependence, chiral and continuum extrapolations can be resolved & estimated to give g S to 10%

13. Excited States Statistics & better interpolating operators –Improve overlap with ground state of (p,n) operators Simulations at many Δt –Needed to eliminate excited state contribution 13 np × nn Δt =t f - t i =t p - t n Γ(t)

14. Signal in the ratio 14 The calculation of g S will dictate the statistics needed One-state versus two-state fit

15. Scalar channel g S : Signal versus Δt, t 15 Δt = 8 9 10 11 12 Δt=10 (~1.2 fm) is the best compromise 1013 conf

16. Tensor channel g T : Signal versus Δt 16 Δt = 8 9 10 11 12 No significant Δt dependence

17. Reducing excited state contamination Simultaneous fit to all Δt =t f - t i 17 Assuming 1 excited state, the 3-point function behaves as Where M 0 and M 1 are the masses of the ground & excited state and A 0 and A 1 are the corresponding amplitudes. np × titi ttftf

18. Simultaneous fit to all Δt 18 Δt=8Δt=10Δt=12 Data for g S on the M π =220 MeV ensemble at a=0.12fm TermExcluding

19. Simultaneous fit to all Δt 19 Δt=10Δt=12Δt=14 Data for g S on the M π =220 MeV ensemble at a=0.09fm TermExcluding

20. Uncertainty in the chiral extrapolation 20 Do chiral logs dominate at lower M π 2 ? What M π 2 interval should be used in the extrapolation?

21. Reducing uncertainty in the chiral extrapolation 21 Ongoing simulations

22. Renormalization of bilinear operators Non-perturbative renormalization Z Γ using the RI-sMOM scheme – Need quark propagator in momentum space Results – 101 lattices at a=0.12 fm M π =310 – 60 lattices at a=0.12 fm M π =220 22 × Γ > >

23. ZAZA 23 M π = 310 MeV 220 MeV

24. Z S ( in MS scheme at 2 GeV ) 24 M π = 310 MeV 220 MeV

25. Z T ( in MS scheme at 2 GeV) 25 M π = 310 MeV 220 MeV

26. Renormalization constants Z Γ Largest uncertainty: – O(a) errors due to full rotational symmetry → cubic symmetry – Examine p 4 versus (p 2 ) 2 behavior Data show (~0.05) variation at fixed p 2 Z A, Z S and Z T are all between 0.95–1.0 with < 1% error – HYP smearing brings the Z Γ close to unity Z Γ → 1 as a → 0 26

27. Results PNDME Collaboration g A = 1.214(40) g S = 0.66(24) g T = 1.094(48) LHPC g A = 1.0-1.2 g S = 1.08(28)(16) g T = 1.038(11)(12) 27

28. g S and g T 28

29. Continuum extrapolation Need estimates at a = 0.12, 0.09, 0.06 fm to perform a continuum extrapolation of renormalized charges (g R = g bare × Z) Will need >1000 configurations at a=0.12, 0.09 and 0.06 fm to quantify if g S and g T have significant a dependence and get estimates with 10% uncertainty 29

30. Summary GOAL: To use experimental measurements of b and b-b ν at the 10 -3 level to bound ε S and ε T requires calculation of g T and g S at the 10-20% level 2011: Lattice QCD estimates of g S and g T improved the bounds on ε S and ε T compared to previous estimates based on phenomenological models 2013: Lattice calculations are on track to providing g T and g S with 10-20% uncertainty 30

31. β-decay versus LHC constraints 31 LHC @ 14TeV and 300fb -1, will provide comparable constraints to low-energy ones with δg S /g S ~15%

32. Acknowledgements Computing resources from –USQCD –XSEDE –LANL 2+1+1 HISQ lattices generated by the MILC collaboration Computer code uses CHROMA library Supported by DOE and LANL-LDRD 32