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Introduction U ( 3 ) 5 Invariant Operators Comments On Non- U ( 3 ) 5 Invariant Operators Constraining New Physics with Combined Low and High Energy Observables A combined effective operator analysis of precision data James Jenkins Theoretical

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Introduction U(3)5 Invariant Operators Comments On Non-U(3)5 Invariant Operators

Constraining New Physics with Combined Low and High Energy Observables

A combined effective operator analysis of precision data James Jenkins

Theoretical Division, T-2 Los Alamos National Laboratory

2009 Phenomenology Symposium, Madison, WI

James Jenkins Low & High Energy Constraints

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Introduction U(3)5 Invariant Operators Comments On Non-U(3)5 Invariant Operators

Outline

1

Introduction Operator Set Observables

2

U(3)5 Invariant Operators Global Analysis Individual Operator Analysis

3

Comments On Non-U(3)5 Invariant Operators

James Jenkins Low & High Energy Constraints

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Introduction U(3)5 Invariant Operators Comments On Non-U(3)5 Invariant Operators Operator Set Observables

Operator Set

U(3)5 Invariant Operators

OWB = (h†σah)W a

µνBµν, Oh = |h†Dµh|2

ℓℓ =

1 2 (ℓγµℓ)(ℓγµℓ), Os

ℓq = (ℓγµℓ)(qγµq),

ℓq = (ℓγµσaℓ)(qγµσaq),

Oℓe = (ℓγµℓ)(eγµe), Oqe = (qγµq)(eγµe), Oℓu = (ℓγµℓ)(uγµu), Oℓd = (ℓγµℓ)(dγµd), Oee = 1 2 (eγµe)(eγµe), Oeu =(eγµe)(uγµu), Oed =(eγµe)(dγµd). Os

hℓ =i(h†Dµh)(ℓγµℓ) +h.c., Ot hℓ =i(h†Dµσah)(ℓγµσaℓ) +h.c.,

hq =i(h†Dµh)(qγµq) +h.c., Ot hq =i(h†Dµσah)(qγµσaq) +h.c.,

Ohu =i(h†Dµh)(uγµu) +h.c., Ohd =i(h†Dµh)(dγµd) +h.c., Ohe =i(h†Dµh)(eγµe) +h.c. OW = ǫabc W aν

µ W bλ ν

W cµ

These interfere with dominant Standard Model processes

James Jenkins Low & High Energy Constraints

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Introduction U(3)5 Invariant Operators Comments On Non-U(3)5 Invariant Operators Operator Set Observables

Operator Anatomy

Each operator is associated with a dimensionless coupling constant ai

v2 Oi

ai = v2 Λ2

i

× T flavor

a,b...

Operators will shift parameters (α, MZ, GF...) and contribute to physical processes directly. Goal is to calculate corrections to observables (linear in ai) and bound operators:

Globally Using individual operators We Use v = 174 GeV

James Jenkins Low & High Energy Constraints

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Introduction U(3)5 Invariant Operators Comments On Non-U(3)5 Invariant Operators Operator Set Observables

Precision Observables

Included Measurements Weak charge in Cs and Tl (Atomic Parity Violation) Neutrino Deep Inelastic Scattering (DIS) data (NuTeV) Z-Pole Observables LEP2 fermion pair production W pair production differential cross-sections W mass measurements From this, we create a χ2 function quadratic in ai parameters. This contains 237 (generally correlated) terms!

Our global analysis is extended from a Mathematica Notebook by Han & Skiba, 2005 James Jenkins Low & High Energy Constraints

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Introduction U(3)5 Invariant Operators Comments On Non-U(3)5 Invariant Operators Operator Set Observables

Added low energy observable: ∆CKM

Consider the unitarity of the CKM matrix. We write: |Vud|2 + |Vus|2 + |Vub|2 ≡ 1 + ∆CKM, where the deviation from unitarity receives contributions as ∆CKM = 2

(ahq3 − ahl3) − (alq3 − all3)
.

This is experimentally constrained to be ∆CKM = (−2 ± 6) × 10−4 (Dominant Superallowed Modes) ∆CKM constrains operators

Os

ℓℓ = 1

2(ℓγµℓ)(ℓγµℓ), Ot

ℓq = (ℓγµσaℓ)(qγµσaq),

Ot

hℓ =i(h†Dµσah)(ℓγµσaℓ) +hc., Ot hq =i(h†Dµσah)(qγµσaq) +hc.

James Jenkins Low & High Energy Constraints

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Introduction U(3)5 Invariant Operators Comments On Non-U(3)5 Invariant Operators Global Analysis Individual Operator Analysis

Simple Error Propagation

Maximum deviation of a quantity composed of n observables: (δ∆CKM))2 =

n

∂∆CKM ∂ai ∂∆CKM ∂aj Mijδaiδaj. Plugging in numbers from precision data yields δ∆CKM = 2.94 × 10−3. This is 4.8 times larger than the experimentally extracted ∆CKM uncertainty of 6 × 10−4!

James Jenkins Low & High Energy Constraints

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Introduction U(3)5 Invariant Operators Comments On Non-U(3)5 Invariant Operators Global Analysis Individual Operator Analysis

Allowed Contours

Alternate value: ∆CKM = −0.0025 ± 0.0006

James Jenkins Low & High Energy Constraints

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Introduction U(3)5 Invariant Operators Comments On Non-U(3)5 Invariant Operators Global Analysis Individual Operator Analysis

Pseudo-Pull Plot

Contributions from various measurement types

James Jenkins Low & High Energy Constraints

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Introduction U(3)5 Invariant Operators Comments On Non-U(3)5 Invariant Operators Global Analysis Individual Operator Analysis

Observable Correlations

Assuming the dominance of a single operator Oi, we substitute ai for ∆CKM using ai = ±1

2∆CKM

This leads to direct correlations between any two observables! In particular, the χ2 functions become simple quadratics:

Measurement

χ2

Os ℓℓ Ot ℓq Ot

hℓ

∆CKM

0.11 1.2e3∆ + 2.8e6∆2 1.2e3∆ + 2.8e6∆2 1.2e3∆ + 2.86∆2 1.2e3∆ + 2.8e6∆2 MW 0.65

−2.4e2∆ + 2.7e3∆2 −4.7e2∆ + 1.1e5∆2

Zline 0.96

−2.2e1∆ + 6.8e4∆2

6.9e1∆ + 3.3e5∆2 1.5e2∆ + 2.2e5∆2 bc 0.90 3.6e2∆ + 6.8e3∆2 4.7e2∆ + 8.1e3∆2 8.0e0∆ + 8.2e1∆2 pol 0.98

−3.3e2∆ + 8.2e4∆2 −4.3e2∆ + 1.4e5∆2

QFB 0.57 2.1e2∆ + 1.8e4∆2 2.6e2∆ + 3.1e4∆2 DIS 1.27 9.1e1∆ + 1.9e3∆2 6.1e1∆ + 9.6e2∆2 1.9e2∆ + 8.2e3∆2 6.1e1∆ + 9.6e2∆2 QW 0.54 1.3e0∆ + 1.8e0∆2 2.6e1∆ + 3.1e2∆2

−7.9e1∆ + 2.9e3∆2

2.6e1∆ + 3.1e2∆2 hadLEP 0.66

−3.5e1∆ + 1.3e3∆2

1.2e2∆ + 1.6e4∆2

−4.3e1∆ + 2.0e3∆2 −2.2e1∆ + 5.4e2∆2 µLEP

0.85 2.2e1∆ + 1.3e3∆2 1.1e0∆ + 5.4e0∆2

τLEP

0.85

−4.1e − 1∆ + 8.2e2∆2

9.1e − 3∆ + 3.3e0∆2 eOPAL 0.77

−7.4e − 1∆ + 2.4e1∆2

9.1e − 1∆ + 1.9e − 1∆2 WL3 1.09 7.2e0∆ + 1.3e2∆2 9.1e − 1∆ + 6.8e0∆2

−1.6e0∆ + 6.3e0∆2

tot 0.86 7.4e0∆ + 1.8e4∆2 1.3e1∆ + 1.2e4∆2 7.8e0∆ + 3.0e4∆2 1.7e1∆ + 1.9e4∆2

James Jenkins Low & High Energy Constraints

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Introduction U(3)5 Invariant Operators Comments On Non-U(3)5 Invariant Operators Global Analysis Individual Operator Analysis

Individual Operator Constraints

James Jenkins Low & High Energy Constraints

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Introduction U(3)5 Invariant Operators Comments On Non-U(3)5 Invariant Operators Global Analysis Individual Operator Analysis

Individual Operator Constraints

James Jenkins Low & High Energy Constraints

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Introduction U(3)5 Invariant Operators Comments On Non-U(3)5 Invariant Operators Global Analysis Individual Operator Analysis

Z-Line Correlations (Light Fermions)

James Jenkins Low & High Energy Constraints

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Introduction U(3)5 Invariant Operators Comments On Non-U(3)5 Invariant Operators Global Analysis Individual Operator Analysis

Z-Pole Polarized Lepton Asymmetries

James Jenkins Low & High Energy Constraints

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Introduction U(3)5 Invariant Operators Comments On Non-U(3)5 Invariant Operators Global Analysis Individual Operator Analysis

Z-Pole Heavy Fermion Observables

James Jenkins Low & High Energy Constraints

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Introduction U(3)5 Invariant Operators Comments On Non-U(3)5 Invariant Operators Global Analysis Individual Operator Analysis

Other Correlations

James Jenkins Low & High Energy Constraints

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Introduction U(3)5 Invariant Operators Comments On Non-U(3)5 Invariant Operators Global Analysis Individual Operator Analysis

DIS Correlation (without NuTeV)

James Jenkins Low & High Energy Constraints

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Introduction U(3)5 Invariant Operators Comments On Non-U(3)5 Invariant Operators Global Analysis Individual Operator Analysis

The NuTeV Anomaly

The Standard Model Lagrangian may be written as: L = −4 √ 2GF

L ¯

νγµPLν + gν

R¯

νγµPRν

L¯

fγµPLf + gf

R¯

fγµPRf

NuTeV constrains the coupling combinations g2

L

= (2gν

Lgu L)2 + (2gν Lgd L )2

g2

R

= (2gν

Lgu R)2 + (2gν Lgd R)2

They find g2

L = 0.30005 ± 0.00137

(EW Fit : 0.3042) g2

R = 0.03076 ± 0.00011

(EW Fit : 0.0301) Usually interpreted as a 3σ deviation in sin2 θw

James Jenkins Low & High Energy Constraints

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Introduction U(3)5 Invariant Operators Comments On Non-U(3)5 Invariant Operators Global Analysis Individual Operator Analysis

NuTeV Correlations

James Jenkins Low & High Energy Constraints

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Introduction U(3)5 Invariant Operators Comments On Non-U(3)5 Invariant Operators Global Analysis Individual Operator Analysis

NuTeV: More Details

δg2

= 1 18(2s2 − 1) n 6s2(2s2 − 1)(alq1 + ahq1) + 2s2(20s4 − 28s2 + 9)(alq3 − ahq3) + 2s2(10s4 − 19s2 + 9)(2ahl3 − all3) − 2ahl1(20s6 − 46s4 + 36s2 − 9) − ah(10s6 − 27s4 + 27s2 − 9) + 2scaWB(9 − 10s2)

Substituting ∆CKM

δg2

L = s2(10s2 − 9)

9 −∆CKM 2 + 1 2s2 − 1 “ s2all3 − ahl3 ”ff .

Plugging in the observed δg2

L and ∆CKM yields the relationship

ahl3 − 0.231all3 = (7.7 − 7.9) × 10−3 This band is outside of the allowed ahl3 − all3 contour!

James Jenkins Low & High Energy Constraints

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Introduction U(3)5 Invariant Operators Comments On Non-U(3)5 Invariant Operators

Comments on Non-U(3)5 Invariant Operators

Non-U(3)5 Invariant Operators

Oqde = (ℓe)(dq) + h.c., Oℓq = (¯ ℓae)ǫab(¯ qbu) + h.c. Ot

ℓq = (¯

ℓaσµνe)ǫab(¯ qbσµνu) + h.c., Ohh = i(hT ǫDµh)(uγµd) + h.c.

These affect a disjoint set of observables (almost). Treating the flavor structure Minimal Flavor Violation (MFV) Mass suppressions Two Higgs Doublet Model tan β enhancement R Parity Violating SUSY Complete freedom A full extension to include these operators is not trivial!

James Jenkins Low & High Energy Constraints

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Introduction U(3)5 Invariant Operators Comments On Non-U(3)5 Invariant Operators

Summary

We combine bounds from high energy precision measurements and low energy observables to constrain new physics. ∆CKM constraints are important

Should be included in future fits Non-trivially modify the allowed global parameter space Yields observable correlations (individual operator approach)

The NuTeV Anomaly

Can’t be resolved by a single operator Can’t be resolved by the (four) ∆CKM operators Can be resolved using all operators

Non-U(3)5 invariant analysis is hard and results are forthcoming!

James Jenkins Low & High Energy Constraints