Electroweak Physics at an Electron-Ion ColliderM.J. Ramsey-MusolfWisconsin-MadisonQuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.

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http://www.physics.wisc.edu/groups/particle-theory/

NPACTheoretical Nuclear, Particle, Astrophysics & Cosmology

ECT* Trento, July 2008

Outline

• Brief Context: Precision and Energy Frontiers

• Neutral Current Processes: PV DIS & PV Moller

• Charged Current Processes: e-+A K ET + j

• Lepton flavor violation: e-+A K - + A

Disclaimer: some ideas worked out in detail; others need more research

Low-Energy: What we have learned

• Weak interactions violate P

• QCD is tiny

• QWP ~ 0.1 QW

n ~ -1

• S-quarks: impt for spin, not for N

• Sin2W runs

• TeV scale technicolor unlikely

• Nuclei have large anapole moments

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What we would like to know

• Does the “new SM” violate CP? Can it explain the abundance of matter?

• Are there new TeV scale interactions? If so, what are their symmetries?

• How does QCD make a proton?

• Are lepton number and charged lepton flavor conserved ?

Precision Probes of New Symmetries

Beyond the SM SM symmetry (broken)

Electroweak symmetry breaking: Higgs ?

New Symmetries

1. Origin of Matter2. Unification & gravity

3. Weak scale stability4. Neutrinos

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?

LHC: energy frontier

Low-energy: precision frontier

EIC: Post LHC Era

Precision & Energy Frontiers

Radiative corrections

Direct Measurements

Stunning SM Success

J. Ellison, UCI

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GFμ

≈ 1+ ΔrZ − Δrμ( )

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• Precision measurements predicted a range for mt

before top quark discovery

• mt >> mb !

• mt is consistent with that range

• It didn’t have to be that way

Probing Fundamental Symmetries beyond the SM:

Use precision low-energy measurements to probe virtual effects of new symmetries & compare with collider results

Precision Frontier:

• Precision ~ Mass scale

• Look for pattern from a variety of measurements

• Identify complementarity with collider searches

• Special role: SM suppressed processes

Nuclei & Charged Leptons

PV Electron ScatteringQuickTime™ and a

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Weak DecaysQuickTime™ and a

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• nuclear decay

• pion decays

• muon decays

• Q-Weak • 12 GeV Moller• PV DIS

Muons

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• g-2

• A->eA

EIC:• More PV• New CC ?• LFV ?

Neutral Current Probes: PV

• Basics of PV electron scattering

• Standard Model: What we know

• New physics ? SUSY as illustration

• Probing QCD

PV Electron Scattering

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Parity-Violating electron scattering

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APV =N↑↑ − N↑↓

N↑↑ + N↑↓

=GFQ2

4 2παQW + F(Q2,θ)[ ]

“Weak Charge” ~ 0.1 in SM

Enhanced transparency to new physics

Small QCD uncertainties (Marciano & Sirlin; Erler & R-M)

QCD effects (s-quarks): measured (MIT-Bates, Mainz, JLab)

Nuclei & Charged Leptons: Theory

PV Electron ScatteringQuickTime™ and a

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• Q-Weak • 12 GeV Moller• PV DIS

Muons

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• g-2

• A->eA

Essential Role for Theory

• Precise SM predictions (QCD)

• Sensitivity to new physics & complementarity w/ LHC

• Substantially reduced QCD uncertainty in sin2W running

• QCD uncertainties in ep box graphs quantified

• Comprehensive analysis of new physics effects

e p e p e p

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• n decay correlations

• nuclear decay

• pion decays

• muon decays

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Effective PV e-q interaction & QW

Low energy effective PV eq interaction

Weak Charge:

Nu C1u + Nd C1d

Proton:

QWP = 2 C1u + C1d = 1-4 sin2W ~ 0.1

Electron:

QWe = C1e = -1+4 sin2W ~ - 0.1

QW and Radiative Corrections

Tree Level

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QWf = gV

f gAe

Radiative Corrections

QWf =ρPV (2I3

f −4QfκPV )+λ fsin2 θW

Flavor-independent

Normalization Scale-dependent effective weak mixing

Flavor-dependent

Constrained by Z-pole precision observables

Large logs in

Sum to all orders with running sin2W & RGE

Weak Charge & Weak Mixing

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sin2 θW =g(μ)Y

2

g(μ)2 + g(μ)Y2

SU(2)LU(1)Y

Weak mixing depends on scale

Weak Mixing in the Standard Model

Scale-dependence of Weak Mixing

SLAC Moller

Parity-violating electron scattering

Z0 pole tension

Z Pole Tension

⇒ mH = 89 +38-28

GeV⇒ S = -0.13 ± 0.10

ALR AFB (Z→ bb)

sin2θw = 0.2310(3)

↓mH = 35 +26

-17 GeVS= -0.11 ± 17

sin2θw = 0.2322(3)

↓mH = 480 +350

-230

GeVS= +0.55 ± 17

Rules out the SM! Rules out SUSY!Favors Technicolor!

Rules out Technicolor!Favors SUSY!

(also APV in Cs) (also Moller @ E158)

W. MarcianoThe Average: sin2θw = 0.23122(17)

3σ apart

•Precision sin2W measurements at colliders very challenging•Neutrino scattering cannot compete statistically•No resolution of this issue in next decade

K. Kumar

Weak Mixing in the Standard Model

Scale-dependence of Weak Mixing

JLab Future

SLAC Moller

Parity-violating electron scattering

Z0 pole tension

Effective PV e-q interaction & PVDIS

Low energy effective PV eq interaction

PV DIS eD asymmetry: leading twistWeak Charge:

Nu C1u + Nd C1d

Proton:

QWP = 2 C1u + C1d = 1-4 sin2W ~ 0.1

Electron:

QWe = C1e = -1+4 sin2W ~ - 0.1

Model Independent Constraints

P. Reimer, X. Zheng

C2q and Radiative Corrections

Tree Level

Radiative CorrectionsFlavor-dependent

Flavor-independent

Normalization Scale-dependent effective weak mixing

Constrained by Z-pole precision observables

Like QWp,e ~ 1 - 4 sin2W

New Physics: Comparing PV Observables

QWP = 0.0716 QW

e = 0.0449

Experiment

SUSY Loops

E6 Z/ boson

RPV SUSY

Leptoquarks

SM SM

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±0.0029

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±0.0040

SUSY Radiative Corrections

Propagator

Box

Vertex & External leg

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SUSY: R Parity-Violation

μ−

ν e e−

νμ

˜ e Rk

12k 12k

e−

d e−

d

˜ q Lj

1j1

1j1

L=1 L=1

Δ12k =λ12k

2

4 2GF M˜ e Rk

2 Δ1j1/ =

λiji/ 2

4 2GFM˜ q Lj

2

• No SUSY DM: LSP unstable

• Neutrinos are Majorana

PVES & APV Probes of SUSY

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Q

WP

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US

Y /

QW

P,

SM

RPV: No SUSY DM Majorana ν s

SUSY Loops

QWe, SUSY / QW

e, SM

g-2

12 GeV

6 GeV

E158

Q-Weak (ep)

Moller (ee)

Kurylov, RM, Su

Hyrodgen APV or isotope ratios

Global fit: MW, APV, CKM, l2,…

Comparing AdDIS and Qw

p,e

e

p

RPV

Loops

Deep Inelastic PV: Beyond the Parton Model & SM

e-

N X

e-

Z* γ*

d(x)/u(x): large x Electroweak test: e-q couplings & sin2W

Higher Twist: qq and qqg correlations

Charge sym in pdfs

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up (x) = dn (x)?

d p (x) = un (x)?

PVDIS & QCD

Low energy effective PV eq interaction

PV DIS eD asymmetry: leading twist

Higher Twist (J Lab)

CSV (J Lab, EIC)

d/u (J Lab, EIC) +

PVDIS & CSV

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up (x) = dn (x)?

d p (x) = un (x)?

•Direct observation of parton-level CSV would be very exciting!•Important implications for high energy collider pdfs•Could explain significant portion of the NuTeV anomaly

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u(x) = up (x) − dn (x)

δd(x) = d p (x) − un (x)

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RCSV =δAPV (x)

APV (x)= 0.28

δu(x) −δd(x)

u(x) + d(x)

Londergan & Murdock

Few percent A/A

Adapted from K. Kumar

PVDIS & d(x)/u(x): xK1

Adapted from K. Kumar

SU(6): d/u~1/2Valence Quark: d/u~0

Perturbative QCD: d/u~1/5

PV-DIS off the proton(hydrogen target)

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APV =GFQ2

2παa(x) + f (y)b(x)[ ]

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a(x) =u(x) + 0.91d(x)

u(x) + 0.25d(x)

Very sensitive to d(x)/u(x)

A/A ~ 0.01

PVES at an EIC

Scale-dependence of Weak Mixing

JLab Future

SLAC Moller

Parity-violating electron scattering

EIC PVDIS ?

Z0 pole tension

EIC Moller ?

Charged Current Processes

• The NuTeV Puzzle

• HERA Studies

• W Production at an EIC ? CC/NC ratios ?

Weak Mixing in the Standard Model

Scale-dependence of Weak Mixing

JLab Future

SLAC Moller

νnucleus deep inelasticscattering

Z0 pole tension

The NuTeV Puzzle

Rν =σνNNC σνN

CC =gL2 +rgR

2

Rν =σν NNC σ ν N

CC =gL2 +r−1gR

2

gL,R2 =

ρνNNC

ρνNCC

⎛

⎝ ⎜ ⎞

⎠ ⎟

2

(εL ,Rq

q∑ )2

r =σνNCC σν N

CC

Rνexp−Rν

SM =−0.0033±0.0007

Rν exp−Rν

SM =−0.0019±0.0016

R− =

Rν −rRν

1−r=(1−2sin2θW) /2+L

Paschos-Wolfenstein

SUSY Loops

RPV SUSY

Wrong sign

Other New CC Physics?

Low-Energy Probes

Nuclear & neutron decay

Pion leptonic decay

Polarized -decay

O / OSM ~ 10-3

O / OSM ~ 10-4

O / OSM ~ 10-2

HERA W production

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O / OSM ~ 10-1

A. Schoning (H1, Zeus)

Lepton Number & Flavor Violation

• LNV & Neutrino Mass

• ν Mechanism Problem

• LFV as a Probe

• K e Conversion at EIC ?

ν-Decay: LNV? Mass Term?

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( )Mass meV

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12 3 4 5 6 7

1 ( )Minimum Neutrino Mass meV

U1e = .866 m2

sol = 7 meV

2

U2e = .5 m2

atm = 2 meV

2

U 3e =

Inverted

Normal

Degenerate

Dirac Majorana

-decayLong baseline

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?

Theory Challenge: matrix elements+ mechanism

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mνEFF & neutrino spectrum

Normal Inverted

ν-Decay: LNV? Mass Term?

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1 ( )Minimum Neutrino Mass meV

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sol = 7 meV

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U2e = .5 m2

atm = 2 meV

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U 3e =

Inverted

Normal

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Dirac Majorana

-decayLong baseline

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?

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mνEFF & neutrino spectrum

Normal Inverted

See-saw mechanism

Leptogenesis

νL νLνR

H H

Lepton Asym ! Baryon Asym

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GERDA CUORE

EXO Majorana

ν-Decay: Mechanism

Dirac Majorana

Theory Challenge: matrix elements+ mechanism

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Mechanism: does light νM exchange dominate ?

How to calc effects reliably ? How to disentangle H & L ?

O(1) for ~ TeV Does operator power counting suffice?

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ν-Decay: Interpretation

0.1

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( )Mass meV

12 3 4 5 6 7

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12 3 4 5 6 7

1 ( )Minimum Neutrino Mass meV

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sol = 7 meV

2

U2e = .5 m2

atm = 2 meV

2

U 3e =

Inverted

Normal

Degenerateν signal equivalent to degenerate hierarchy

Loop contribution to mν of inverted hierarchy scale

Lepton Flavor & Number Violation

Present universe Early universe

Weak scale Planck scale

log10(μ / μ0)

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MEG: γ ~ 5 x 10-14

2e: B ->e ~ 5 x 10-17

??

R = B->e

B->eγ

Also PRIME

Lepton Flavor & Number Violation

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MEG: B->eγ ~ 5 x 10-14

2e: B->e ~ 5 x 10-17

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Logarithmic enhancements of R

Low scale LFV: R ~ O(1) GUT scale LFV: R ~ Oα

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0ν decay

Light νM exchange ?

Heavy particle exchange ?

Raidal, Santamaria; Cirigliano, Kurylov, R-M, Vogel

k11/ ~ 0.09 for mSUSY ~ 1 TeV

->eγ LFV Probes of RPV:

k11/ ~ 0.008 for mSUSY ~ 1 TeV

->e LFV Probes of RPV:

mν “naturalness”:

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Lepton Flavor & Number Violation

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Exp: B->eγ ~ 1.1 x 10-7

EIC: ~ 103 | A1e|2 fb

Raidal, Santamaria; Cirigliano, Kurylov, R-M, Vogel

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Logarithmic enhancements of R

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|A2e|2 < 10-8

EIC: ~ 10-5 fb

If |A1e|2 ~ |A2

e|2

Log enhancement:

|A1e|2 / |A2

e|2 ~ | ln me / 1 TeV |2 ~ 100

BKeγ 48 3 α |A2e|2

Need ~ 1000 fb

LFV with leptons: HERA

Veelken (H1, Zeus) (2007)

Leptoquark Exchange

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qq eff op

lq|2 < 10-4 (MLQ / 100 GeV)2

Induce Keγ at one loop?

LFV with leptons: recent theory

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Kanemura et al (2005)

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qq eff opSUSY Higgs Exchange

lq|2 < 2 x 10-2 (MLQ / 100 GeV)2

lq|2 < 10-4 (MLQ / 100 GeV)2 HERA

Summary

• Precision studies and symmetry tests are poised to discovery key ingredients of the new Standard Model during the next decade

• There may be a role for an EIC in the post-LHC era

• Promising: PV Moller & PV DIS for neutral currents

• Homework: Charged Current probes -- can they complement LHC & low-energy studies?

• Intriguing: LFV with eK conversion:

€

L dt ~ 103 fb∫

Thank you !

• Precision studies and symmetry tests with neutrons are poised to discovery key ingredients of the new Standard Model during the next decade

• Physics “reach” complements and can even exceed that of colliders: dn~10-28 e-cm ; O/OSM ~ 10-4

• Substantial experimental and theoretical progress has set the foundation for this era of discovery

• The precision frontier is richly interdisciplinary: nuclear, particle, hadronic, atomic, cosmology

To the organizers, ECT* staff, and participants for a lively and stimulating workshop

Back Matter

• Precision studies and symmetry tests with neutrons are poised to discovery key ingredients of the new Standard Model during the next decade

• Physics “reach” complements and can even exceed that of colliders: dn~10-28 e-cm ; O/OSM ~ 10-4

• Substantial experimental and theoretical progress has set the foundation for this era of discovery

• The precision frontier is richly interdisciplinary: nuclear, particle, hadronic, atomic, cosmology