Weak Decays: theoretical overview Vincenzo Cirigliano Los Alamos - - PowerPoint PPT Presentation

Vincenzo Cirigliano Los Alamos National Laboratory

ACFI workshop on Fundamental Symmetry Tests with Rare Isotopes Amherst, October 23-25 2014

Weak Decays: theoretical overview

Outline

• Introduction: beta decays and new physics
• Theoretical framework: from TeV to nuclear scales
• (Quick) overview of probes and opportunities
• Connection with high-energy landscape
• Conclusions

Beta decays and new physics

β-decays and the making of the SM

Fermi, 1934 Lee and Yang, 1956 Feynman & Gell-Mann + Marshak & Sudarshan 1958 Glashow, Salam, Weinberg

p n ν e

Parity conserving: VV, AA, SS, TT ... Parity violating: VA, SP , ...

W u d ν e

Current-current, parity conserving

p n ν e ?

It’s (V-A)*(V-A) !! Embed in non-abelian chiral gauge theory, predict neutral currents

β-decays and the making of the SM

Fermi, 1934 Lee and Yang, 1956 Feynman & Gell-Mann + Marshak & Sudarshan 1958 Glashow, Salam, Weinberg

p n ν e

Parity conserving: VV, AA, SS, TT ... Parity violating: VA, SP , ...

W u d ν e

Current-current, parity conserving

p n ν e ?

It’s (V-A)*(V-A) !! Embed in non-abelian chiral gauge theory, predict neutral currents

... of course with essential experimental input!

β-decays and BSM physics

• In the SM, W exchange (V-A, universality)

• BSM: sensitive to tree-level and loop corrections from large class of

models → “broad band” probe of new physics

• Name of the game: precision! To probe BSM physics at scale Λ, need
• expt. & th. at the level of (v /Λ)2: ≤10-3 is a well motivated target

β-decays and BSM physics

• In the SM, W exchange (V-A, universality)

Theoretical framework

Theoretical Framework

• How do we connect neutron and nuclear beta-decay observables to

short-distance physics (W exchange + BSM-induced interactions)?

• This is a multi-scale problem!
• Best tackled within Effective Field Theory

Λ

(~TeV)

E ΛH

(~GeV)

Nuclear scale

Perturbative matching BSM dynamics involving new particles with m > Λ

Theoretical Framework

• At scale E~MBSM > MW “integrate out” new heavy particles:

generate operators of dim > 4 (this can be done for any model) W,Z

Λ

(~TeV)

E ΛH

(~GeV)

Nuclear scale

Perturbative matching BSM dynamics involving new particles with m > Λ Non-perturbative matching

H = π, n, p

Theoretical Framework

• At hadronic scale E ~ 1 GeV match to description in terms
• f pions, nucleons (+ e,γ) ⇔ take hadronic matrix elements

W,Z

Λ

(~TeV)

E ΛH

(~GeV)

Nuclear scale

Perturbative matching BSM dynamics involving new particles with m > Λ Non-perturbative matching

H = π, n, p Nuclear matrix elements ⇒

• bservables

Non-perturbative

(A,Z)

Theoretical Framework

e

ν

W,Z

• Any new physics encoded in ten leading (dim6) quark-level couplings

Linear sensitivity to εi (interference with SM) Quadratic sensitivity to εi (interference suppressed by mν/E)

~

Quark-level interactions

function of new model-parameters

Matrix elements

• To disentangle short-distance physics, need hadronic and nuclear

matrix elements of SM (at <10-3 level) and BSM operators

• Tools (for nucleons and nuclei):
• symmetries of QCD
• lattice QCD
• nuclear structure

Nucleon matrix elements

• Need the matrix elements of quark bilinears between nucleons
• Given the small momentum transfer in the decays q/mn ~10-3,

can organize matching according to power counting in q/mn

• At what order do we stop? Work to 1st order in

εL,R,S,P

,T ~ 10-3

q/mn ~10-3 α/π ~10-3

• Include O(q/mn) and radiative corrections only for SM operator
• S. Weinberg 1958, B. Holstein ‘70s, ... Gudkov et al 2000’s

• A closer look at

V, A matrix elements (SM operators):

Weinberg 1958

• A closer look at

V, A matrix elements (SM operators):

• Vanish in the isospin limit, hence are O(q/mn) [calculable].

Since they multiply q/mn can neglect them

• Pseudo-scalar bilinear is O(q/mn): since it multiplies q/mn, can

neglect it (but form factor is known, so this can be included)

• The weak magnetism form factor is related to the difference
• f proton and neutron magnetic moments, up to isospin-breaking

corrections

Weinberg 1958

Nuclear matrix elements

• Correspondence

with neutron decay:

→

Holstein 1974

lepton current

Nuclear matrix elements

→

Holstein 1974

• Form factors a(q2), c(q2), ... can be expressed in terms of

nucleon form factors gn(q2) and nuclear matrix elements of appropriate operators (see extra slides)

Overview of probes

a(gA, εα), A(gA, εα) , B(gA, εα), ... isolated via suitable experimental asymmetries

How do we probe the ε’s?

• Rich phenomenology, two classes of observables:

Lee-Yang, Jackson-Treiman-Wyld

• 1. Differential decay rates (probe non

V-A via “b” and correlations)

• 2. Total decay rates (probe mostly

V, A via extraction of Vud, Vus)

Channel-dependent effective CKM element

• Rich phenomenology, two classes of observables:

How do we probe the ε’s?

• 1. Differential decay rates (probe non

V-A via “b” and correlations)

Snapshot of the field

• This table

summarizes a large number of measurements and th. input

• Already quite

impressive. Effective scales in the range Λ= 1-10 TeV (ΛSM ≈ 0.2 TeV)

VC, S.Gardner, B.Holstein 1303.6953 Gonzalez-Alonso & Naviliat-Cuncic 1304.1759

Snapshot of the field

• This table

summarizes a large number of measurements and th. input

• Already quite

impressive. Effective scales in the range Λ= 1-10 TeV (ΛSM ≈ 0.2 TeV)

• Focus on probes

that depend on the ε‘s linearly

VC, S.Gardner, B.Holstein 1303.6953 Gonzalez-Alonso & Naviliat-Cuncic 1304.1759

CKM unitarity: input

Vud

0+→0+ neutron gA = 1..2701(25) T=1/2 mirror Pion beta decay

CKM unitarity: input

Vud

0+→0+ neutron gA = 1..2701(25) T=1/2 mirror Pion beta decay τn= 880 s τn= 888 s

• Extraction dominated by 0+→0+ transitions. Critical theoretical input:

Vud = 0.97417(21) Hardy-Towner 2014 BOTTLE BEAM

Marciano-Sirlin ‘06

Nucleon-level non-log-enhanced radiative correction Isospin breaking in the nuclear matrix element:

CKM unitarity: input

Vud

0+→0+ neutron gA = 1..2701(25) T=1/2 mirror Pion beta decay τn= 880 s τn= 888 s Czarnecki, Marciano, Sirlin 2004

• Neutron decay not yet competitive:

Vud = 0.97417(21) Hardy-Towner 2014 BOTTLE BEAM

• Extraction dominated by 0+→0+ transitions. Critical theoretical input:

Vus

τ→ Kν K→ μν K→ πν τ→ s inclusive CKM unitarity (from Vud)

• Improved LQCD calculations have led to smaller

Vus from K→ πν

mπ → mπphys, a → 0, dynamical charm

FK/Fπ = 1.1960(25) [stable] Vus / Vud = 0.2308(6) f+K→π(0)= 0.959(5) → 0.970(3) Vus = 0.2254(13) → 0.2232(9)

FLAG 2013 + MILC 2014

CKM unitarity: input

Vus from K→ μν Vus from K→ πlν

• No longer perfect agreement with SM. This could signal:
• New physics in εR,P(s) (Kl2 vs Kl3) and in εL+εR , εL,R(s) (ΔCKM)
• Systematics in data** or theory: δC (A,Z), f+(0), FK/Fπ

ΔCKM = - (4 ± 5)∗10-4 0.9 σ ΔCKM = - (12 ± 6)∗10-4 2.1 σ

Vus Vud

K→ μν K→ πlν u n i t a r i t y

CKM unitarity: test

• Given high stakes (0.05% EW test), compelling opportunities emerge:
• Impact on other phenomenology

δτn ~ 0.35 s δτn/τn ~ 0.04 % δgA/gA ~ 0.025% (δa/a , δA/A ~ 0.1%)

• Robustness of δC and rad.corr: nucl. str. calculations + exp. validation
• Pursue

Vud @ 0.02% through neutron decay aCORN, Nab, UCNA+, ... BL2, BL3 (cold beam), UCNτ, ...

• Pursue

Vud through mirror nuclear transitions

CKM unitarity: opportunities

Scalar and tensor couplings

C U R R E N T

• Current most sensitive probes**:

Bychkov et al, 2007

• 2.0×10-4 < fT εT < 2.6 ×10-4

fT = 0.24(4) π → e ν γ

• 1.0×10-3 < gS εS < 3.2×10-3

0+ →0+ (bF)

Towner-Hardyl, 2010

bF , π→eνγ

Quark model: 0.25 < gS < 1

** For global analysis see Wauters et al, 1306.2608

Scalar and tensor couplings

C U R R E N T

• Current most sensitive probes**:

Bychkov et al, 2007

• 2.0×10-4 < fT εT < 2.6 ×10-4

fT = 0.24(4) π → e ν γ

• 1.0×10-3 < gS εS < 3.2×10-3

0+ →0+ (bF)

Towner-Hardyl, 2010

bF , π→eνγ

Quark model: 0.25 < gS < 1 Lattice QCD: 0.91 < gS < 1.13

Impact of improved theoretical calculations using lattice QCD

• R. Gupta et al. 2014

Bhattacharya, et al 1110.6448

** For global analysis see Wauters et al, 1306.2608

Scalar and tensor couplings

F U T U R E

bF , π→eνγ bn , Bn bGT Quark model: 0.25 < gS < 1 0.6 < gT < 2.3

Nab, UCNB,

6He,

...

• Several precision measurements on the horizon (neutron & nuclei)
• For definiteness, study impact of bn, Bn @ 10-3; bGT (6He, ...) @10-3

Herczeg 2001

Additional studies at FRIB?

Scalar and tensor couplings

F U T U R E

bF , π→eνγ bn , Bn bGT

• Can dramatically improve existing limits on εT, probing ΛT ~ 10 TeV

Lattice QCD 2014 0.91 < gS < 1.13 1.0 < gT < 1.1

• R. Gupta et al. 2014

ΛS = 5 TeV

Nab, UCNB,

6He,

...

• Several precision measurements on the horizon (neutron & nuclei)
• For definiteness, study impact of bn, Bn @ 10-3; bGT (6He, ...) @10-3

Additional studies at FRIB?

Connection with high- energy landscape

Connection with landscape

• The new physics that contributes to εα affects other observables!

dj ui dj ui

• Relative constraining power depends on specific model
• Model-independent statements possible in “heavy BSM” benchmark:

MBSM > TeV → new physics looks point-like at the weak scale

Vertex corrections strongly constrained by Z-pole observables (ΔCKM is at the same level) Four-fermion interactions “poorly” constrained: σhad at LEP would allow ΔCKM ~0.01 and non V-A structures at εi ~ 5%. What about LHC?

VC, Gonzalez-Alonso, Jenkins 0908.1754

LHC constraints

• T. Bhattacharya, VC, et al, 1110.6448
• Heavy BSM benchmark:

all εα couplings contribute to the process p p → e ν + X

• No excess events at high mT ⇒ bounds on εα (at the 0.3% -1% level)

β decays vs LHC reach

0% 0.3% 0.6% 0.9% 1.2% 1.5%

β decays LHC

0% 3.0% 6.0% 9.0% 12.0% 15.0%

VC, Gonzalez-Alonso, Graesser, 1210.4553

LHC: √s = 7 TeV L = 5 fb-1 LHC reach already stronger than low-energy Unmatched low- energy sensitivity and future reach LHC limits close to low-energy. Interesting interplay in the future

x x _

All ε’s in MS @ μ = 2 GeV

_

Bhattacharya, et al 1110.6448 Updated with 2014 lattice input

• β-decays (b,B) @ 0.1% can be more constraining than LHC!

Quark model vs LQCD matrix elements LHC: √s = 14 TeV L = 10, 300 fb-1 F U T U R E

Connection to models

• Model → set overall size and pattern of effective couplings
• Beta decays can play very useful diagnosing role

WR H+

u e d ν LQ

“DNA matrix”

...

YOUR FAVORITE MODEL

...

• Qualitative picture:

Can be made quantitative

• MSSM: Distinctive correlation between Cabibbo universality (CKM)

and lepton universality, controlled by sfermion spectrum

• Post-LHC effects are at the few*10-4 level

After LHC constraints

Bauman, Erler, Ramsey- Musolf, arXiv:1204.0035

Light selectrons, heavy squarks & smuons Light squarks, heavy sleptons Light smuons, heavy squarks & selectrons Future 1-sigma Present 1-sigma

• MSSM: Light but compressed SUSY spectrum?
• “invisible” at the LHC
• Can lead to ΔCKM > 10-4

CMS: SUS-11-016- pas

• !CKM > 10-4

Bauman, Pitschmann, Erler, Ramsey-Musolf, preliminary

• Leptoquarks: ΔCKM constraint vs direct searches at HERA and LHC

Pair production at LHC

λ λ

Single production at HERA (depends on λ)

95% CL limits S0 (3,1,1/3)

• Leptoquarks: ΔCKM constraint vs direct searches at HERA and LHC

95% CL limits ΔCKM constraint is stronger (for all four LQ that contribute to ΔCKM)

λ λ

S0 (3,1,1/3)

Conclusions

• Precise (<0.1%) beta decays: “broad band” probe of new physics.

Discovery potential depends on the underlying model

• Both in the “heavy BSM” benchmark and within specific models,

a discovery window exists well into the LHC era!

• Currently, nuclear decays provide strongest constraints on non-

standard couplings (εL+εR, εS, εT)

• General guideline for selection of future probes @ FRIB:
• experimental feasibility
• “theoretical feasibility”: need reliable calculations of recoil
• rder effects and structure-dependent radiative corrections

Future prospects for ΔCKM

• Lowering error on ΔCKM to 10-4 requires factor of 3-4

improvement in Vud and Vus

• Need to overcome following issues:
• Vud : radiative corrections and IB in matrix element
• Vus : K matrix elements from lattice QCD need to improve by

factor of ~3 (may be doable in next 5 years). However, experimental input from K decays currently implies δ(ΔCKM) ~ 2∗10-4 Seems more realistic goal

Extra slides

Coulomb distortion

• f wave-functions

Nucleus-dependent

• rad. corr.

(Z, Emax ,nuclear structure) Nucleus-independent short distance rad. corr.

Sirlin-Zucchini ‘86 Jaus-Rasche ‘87 Towner-Hardy Ormand-Brown Marciano-Sirlin ‘06

Vud from 0+→ 0+ nuclear β decays

Scalar and tensor couplings

F U T U R E

• Fit to decay parameters must include gA (correlations!),

and must account for theory uncertainties at recoil order

• Lattice QCD (n) and nuclear calculations can reduce

recoil-order uncertainty to negligible level

• S. Gardner,
• B. Plaster 2013

Fit to Monte Carlo pseudo-data of “a” and “A” with εT at its current limit

gA

More on matrix elements

Nucleon matrix elements

• Need the matrix elements of quark bilinears between nucleons
• Given the small momentum transfer in the decays q/mn ~10-3,

can organize matching according to power counting in q/mn

• At what order do we stop? Work to 1st order in

εL,R,S,P

,T ~ 10-3

q/mn ~10-3 α/π ~10-3

• Include O(q/mn) and radiative corrections only for SM operator
• B. Holstein ‘70s, ... Gudkov et al 2000’s

• General matching

Weinberg 1958

• General matching

Weinberg 1958

• Need all other form-factors at q2 = 0

• A closer look at

V, A matrix elements (SM operators):

• Vanish in the isospin limit, hence are O(q/mn). Since they multiply

q/mn can neglect them

• Pseudo-scalar bilinear is O(q/mn): since it multiplies q/mn, can

neglect it

• The weak magnetism form factor is related to the difference
• f proton and neutron magnetic moments, up to isospin-breaking

corrections

Weinberg 1958

What do we know about gV,A,S,T ?

• gV = 1 (CVC) up to 2nd order corrections in (mu - md)
• (1-2εR)*gA can be extracted from neutron decay measurement.

LQCD calculation of gA are at the ~10-15% level

Ademollo-Gatto Berhends-Sirlin

• No phenomenological handle on gS; some (quite uncertain yet) info
• n gT, from polarized structure function of nucleon: need LQCD!

Connection to Lee-Yang

• Ignoring recoil order

corrections, one recovers Lee-Yang effective Lagrangian

• The couplings are

expressed in terms

• f gi and εi

Nuclear matrix elements

• Correspondence

with neutron decay:

→

Holstein 1974

• Nuclear form factors can be expressed in terms of nucleon form

factors gn(q2) and nuclear matrix elements of appropriate operators

Holstein 1974

• Nuclear form factors can be expressed in terms of nucleon form

factors gn(q2) and nuclear matrix elements of appropriate operators

Holstein 1974

• Nuclear matrix elements: