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

1LAUR-12-20208

Theory and Experimental effort centered at LANL

• 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)

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PRD85:5 (2012) 054512 arXiv:1110.6448 arXiv:1306.5435

Precision calculations of gS, gT

using Lattice QCD

gT ~

gS ~

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Goal: 10-20% accuracy

XBSM

T. Bhattacharya, S. Cohen, R. Gupta, H-W Lin, A. Joseph

Impact of reducing errors in gS and gT from 50→10%

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|B1-b| < 10-3

|b| < 10-3

b0+ = 2.6 (4.3)∗10-3

Allowed region in [εS , εT ] (90% contours)

gT ~

gS ~

Expt. input

Limited by precision of ME

• 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 RIsmom scheme

Lattice QCD calculation of <p|u Γd|n>Oi

q

n p×

Isolate the neutron e-

Mnτ

Project on the proton e-

Mpτ

ud

uud d

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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

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n p×tsep

Sequential propagators with

nucleon insertion at p=0

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p pu

d

uO(p,t)

Initial inversion of Dirac operator with smeared source

Sequential inversion with (n,p) insertion at p=0

2+1+1 flavor HISQ lattices: goal 1000 configs

• ms set to its physical value using Mss

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a(fm) ml/ms LatticeVolume

Mπ L Mπ (MeV) Configs. Analyzed

0.12 0.2 243 × 64 4.54 305 1013/1013

0.12 0.1 323 × 64 4.29 217 958/958

0.09 0.2 323 × 96 4.5 313 881/1000

0.09 0.1 483 × 96 4.73 220 890/1000

0.06 0.2 483 × 144 4.53 320 800/1000

0.06 0.1 643 × 144 4.28 229 0/1000

Issues in Analysis

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Signal in 2-point baryon correlators

a = 0.12 fm lattices with Mπ = 310 MeV

(Total of 1013 Configurations, each with 4 sources)10

SS

: E

ffec

tive

Mas

s P

lot M

eff

507 Conf 506 Conf 1013 conf

2-point function → MN

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Findings at a=0.12 fm with Mπ=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 gΓ between 2 subsets ≈ Δt dependence

– Signal improves as a → 0

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Need > 4x1000 configurations before tsep dependence, chiral and continuum extrapolations

can be resolved & estimated to give gS to 10%

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

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n p×

n nΔt =tf - ti =tp - tn

Γ(t)

Signal in the ratio

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The calculation of gS will dictate the statistics needed

One-state versus two-state fit

Scalar channel gS: Signal versus Δt, t

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Δt = 8 9 10 11 12

Δt=10 (~1.2 fm) is the best compromise

1013 conf

Tensor channel gT: Signal versus Δt

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Δt = 8 9 10 11 12

No significant Δt dependence

Reducing excited state contamination

Simultaneous fit to all Δt =tf - ti

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Assuming 1 excited state, the 3-point function behaves as

Where M0 and M1 are the masses of the ground & excited state and A0 and A1 are the corresponding amplitudes.

n p×

ti t tf

Simultaneous fit to all Δt

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Δt=8 Δt=10 Δt=12

Data for gS on the Mπ=220 MeV ensemble at a=0.12fm

Term

Excluding

Simultaneous fit to all Δt

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Δt=10 Δt=12 Δt=14

Data for gS on the Mπ=220 MeV ensemble at a=0.09fm

Term

Excluding

Uncertainty in the chiral extrapolation

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Do chiral logs dominate at lower Mπ

2 ?

What Mπ2

interval should be used in the extrapolation?

Reducing uncertainty in the chiral extrapolation

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Ongoing simulations

Renormalization of bilinear operators

• Non-perturbative renormalization ZΓ

using the RI-sMOM scheme

– Need quark propagator

in momentum space

• Results

– 101 lattices at a=0.12 fm Mπ=310

– 60 lattices at a=0.12 fm Mπ=220

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×

Γ

> >

ZA

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Mπ = 310 MeV 220 MeV

ZS (in MS scheme at 2 GeV )

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Mπ = 310 MeV 220 MeV

ZT (in MS scheme at 2 GeV)

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Mπ = 310 MeV 220 MeV

Renormalization constants ZΓ • Largest uncertainty:

– O(a) errors due to full rotational symmetry → cubic symmetry

– Examine p4 versus (p2)2 behavior

• Data show (~0.05) variation at fixed p2

• ZA, ZS and ZT are all between 0.95–1.0 with < 1% error

– HYP smearing brings the ZΓ close to unity

• ZΓ → 1 as a → 0

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ResultsPNDME Collaboration

• gA = 1.214(40)

• gS = 0.66(24)

• gT = 1.094(48)

LHPC

• gA = 1.0-1.2

• gS = 1.08(28)(16)

• gT = 1.038(11)(12)

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gS and gT

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Continuum extrapolation

• Need estimates at a = 0.12, 0.09, 0.06 fm

to perform a continuum extrapolation of

renormalized charges (gR = gbare × Z)

• Will need >1000 configurations at a=0.12, 0.09

and 0.06 fm to quantify if gS and gT have

significant a dependence and get estimates with

10% uncertainty

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Summary

• GOAL: To use experimental measurements of b and b-bν

at the 10-3 level to bound εS and εT requires calculation of

gT and gS at the 10-20% level

• 2011: Lattice QCD estimates of gS and gT improved the

bounds on εS and εT compared to previous estimates based

on phenomenological models

• 2013: Lattice calculations are on track to providing

gT and gS with 10-20% uncertainty

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β-decay versus

LHC constraints

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LHC @ 14TeV and 300fb-1, will provide comparable constraints to low-energy ones with δgS/gS ~15%

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

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