Low-Energy Muon Physics et al - High Energy Physics

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Mar 14, 2012 ... resource for physicists. March 14, 2012 ... [David Hertzog, 2010 DNP Meeting] ... Effective operator analysis: R. Erwin et al, hep-ph/0602240,.
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Fundamental Physics with Muons (and Related Topics) Andr´e de Gouvˆea Northwestern University PASI 2012 March 14 and 16, 2012 – University of Buenos Aires

March 14, 2012

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Tentative Outline 1. Brief Introduction to the Intensity Frontier; 2. “Ordinary” Muon Decay; 3. The Electromagnetic Dipole Moments of the Muon; 4. (Charged) Lepton-Flavor Violation; 5. Rare kaon decays.

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The Research Frontiers of Particle Physics

Homework: Fill in the blank

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We have already heard a lot about the Energy Frontier and the Cosmic Frontier, although I suspect the names never came up. I am going to concentrate on the Intensity Frontier. Boundaries are very fuzzy. To me, “The Intensity Frontier consists of research efforts where one aims at probing nature through precision studies of the properties and fundamental interactions of its basic constituents. While many of these efforts – especially the ones pertinent to Fermilab – revolve around particle accelerators, the energy of the accelerator is not ‘as high as possible’ but is rather dictated by the physics question one is interested in addressing. Instead, it is the intensity and “quality” (purity, time and space profile, etc) of the accelerated beam, that determine the reach of intensity frontier experiments. Past, current, and future Intensity Frontier experiments include studies of neutrino oscillations, searches for rare muon, pion, and kaon processes, precision measurements of muon properties, heavy flavor (charm and bottom) factories and the LEP1 experiments (the energy was fixed at a special value, the Z-pole mass).” [AdG, N. Saoulidou, Ann. Rev. Nucl. Part. Sci. 60, 513-538 (2010).]

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There are many things I will (most likely) not talk about. These include • Neutrino physics – see lectures by Boris and Renata; • Heavy Flavor Physics (B-factories, charm physics, taus, etc); • Searches for proton decay; • Searches for very light, very weakly coupled states (para-photons, axion-like particles, sterile neutrinos, etc). There was a very nice meeting on the Intensity Frontier last December in Washington D.C. http://www.intensityfrontier.org

and a long written report is expected by the end of this month. March 14, 2012

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“Who Ordered That?” The muon is the best known unstable fundamental particle. The muon is also the heaviest fundamental particle we can directly work with. It is a unique, priceless resource for physicists.

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“Who Ordered That?” The muon is the best known unstable fundamental particle. The muon is also the heaviest fundamental particle we can directly work with. It is a unique, priceless resource for physicists.

ANS: “We did!”

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[David Hertzog, 2010 DNP Meeting] March 14, 2012

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Northwestern [David Hertzog, 2010 DNP Meeting]

March 14, 2012

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[David Hertzog, 2010 DNP Meeting] March 14, 2012

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“Ordinary” Muon Decay Virtually 100% of the time the muon decays into an electron and two invisible states (neutrinos). µ− → e− νµ ν¯e Given its small mass (compared to that of the W -boson), muon decay can be parameterized by the effective Lagrangian 4GF X γ gαβ (¯ eα Γγ ν) (¯ ν Γγ µβ ) , − √ 2 γ,α,β where α, β = L, R, and γ = S, V, T (ΓS = 1, ΓV

√ = γµ and ΓT = σµν / 2).

γ V In the Standard Model, gLL = 1, while all other gαβ vanish. (V − A).

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γ coefficients can be measured by precision measurements of the electron The gαβ energy spectrum. For example, if one ignores the mass of the neutrino and the electron, and does not measure the electron polarization,

h io G2F m5µ n 2ρ 2δ d2 Γ 2 3(1 − x) + = (4x − 3) ± P ξ cos θ 1 − x + (4x − 3) 2x µ dxd cos θ 192π 3 3 3 ρ, δ, ξ are (some of) the Michel Parameters; Pµ = µ-polarization; θ = angle between Pµ and the e-momentum; x = 2Ee /mµ . γ The Michel parameters are functions of the gαβ , and are sensitive to New Physics. For example, in a left-right model

3 ∆ρ ' − ϑ2LR , 2

∆ξ = −2ϑ2LR − 2



MW MWR

4

. ϑLR = mixing between SM (“left-handed”) W -boson and “right-handed” WR -boson. Current constraints competitive with collider searches. March 14, 2012

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Current constraints from precision muon decay (Michel params ∝ g ∗ g):

[PDG 2011]

• Note that some constraints are not too stringent. • Expectations are very model dependent. • Effective operator analysis: R. Erwin et al, hep-ph/0602240, discusses connections to (Dirac) neutrino masses.

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TWIST Coll. [1010.4998] March 14, 2012

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The Muon Magnetic Dipole Moment ~ = gµ e S. ~ The magnetic moment of the muon is defined by M 2mµ The Dirac equation predicts gµ = 2, so that the anomalous magnetic moment is defined as (note: dimensionless) aµ ≡

gµ − 2 2

In the standard model, the (by far) largest contribution to aµ comes from the one-loop QED vertex diagram, first computed by Schwinger: aQED (1 − loop) = µ

α = 116, 140, 973.5 × 10−11 2π

The theoretical estimate has been improved significantly since then, mostly to keep up with the impressive experimental reach of measurements of the g − 2 of the muon. March 14, 2012

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Some Brief Comments on the Standard Model Computation of aµ

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[hep-ph/0512330]

[talk by A. Czarnecki at CIPANP 2006]

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[talk by A. Czarnecki at CIPANP 2006]

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[New g-2 Collaboration, FERMILAB-PROPOSAL-0989] March 14, 2012

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The precision frontier: can we reliably estimate this? • cannot be evaluated from first principles: perhaps lattice QCD?

(×10−11 )

2009 Consensus: 105±26 March 14, 2012

[arXiv 0901.0306]

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very similar to New Physics! (more on this later)

[talk by A. Czarnecki at CIPANP 2006]

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(±26) [±41]

[New g-2 Collaboration, FERMILAB-PROPOSAL-0989] March 14, 2012

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Spin Precession w.r.t. Momentum Vector

(g-2)/2

# of high E electrons

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NOTE: aLbL = 105 ± 26 × 10−11 µ

[Davier et al, 1010.4180]

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∆aµ : we need to dig a little more!

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New experiment at Fermilab.

IMPORTANT: Theory error expected to improve by factor of 3. March 14, 2012

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Timeline: CD0, CD1 in 2012, start before 2015.

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Sensitivity to New Physics If there is new ultra-violate physics, it will manifest itself, as far as aµ is concerned, via the following effective operator (dimension 6): mµ λH µν µν µ ¯ σ µF → µ ¯ σ µF , µν µν Λ2 Λ2 where Λ is an estimate for the new physics scale. (dependency on muon mass is characteristic of several (almost all?) models. It is NOT guaranteed) Contribution to aµ from operator above is 4m2µ δaµ = eΛ2 Current experimental sensitivity: Λ ∼ 10 TeV. Note that, usually, new physics scale can be much lower due to loop-factors, gauge couplings, etc. In the SM the heavy gauge boson contribution yields 1 eg 2 ∼ 2 2 Λ 16π 2 MW March 14, 2012

m2µ GF −→ δaµ ∼ 4π 2

Not A Bad Estimate!

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Some Examples: • Low energy supersymmetry:

  5α2 + αY m2µ 100 GeV 2 −11 δaµ ' ± tan β ∼ ±100 × 10 tan β, 48π mSUSY m2SUSY where all SUSY particles weigh the same (mSUSY ). A nonzero δaµ translates into an upper bound for mSUSY . • Theory with large extra-dimensions where the right-handed neutrinos propagate on the bulk: 2 m νj g 2 m2µ X 2 −9 δaµ = − |U | ∼ −10 , jµ 2 32π 2 MW ∆m2atm j

where  is a small parameter which depends on the extra-dimensional physics (how many extra-dimensions, how large, etc). Note the “wrong” sign. [AdG, Giudice, Strumia, Tobe, hep-ph/0107156] • In general, need Λ ∼ 10 TeV – as large as the electroweak one. New physics must couples strongly to the muon (or be lighter than the W -boson). March 14, 2012

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(mHHH = dim-6 contribution µ to the muon mass)

[Kannike et al, arXiv:1111.2551]

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Very quick comments on the muon electric-dipole moment, dµ • CP-violating observable; • Predicted to be non-zero-but-tiny in the SM: dµ < 10−36 e-cm. Great place to look for new physics! • Current bounds: dµ < 1.8 × 10−19 e-cm. Compare to de < 10−27 e-cm. • In general, d` ∝ m` , so dµ ∼ de × (mµ /me ). • New g − 2 experiment at FNAL would be sensitive to dµ > 10−21 e-cm. Dedicated effort could reach dµ > 10−24 e-cm. Is it worth it? [yes!] • Same effective operator contributes to aµ and dµ mµ µν µ ¯ σ µF µν Λ2

versus

mµ CP 2 µ ¯σµν γ5 µF µν . Λ

CP measures how much the new physics violates CP. If Λ ∼ 10 TeV, CP  1. March 14, 2012

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Andr´ e de Gouvˆ ea [see 1008.5091 and hep-ph/0108275]

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[T. R¨ uppell, talk at PSI]

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[T. R¨ uppell, talk at PSI]

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Charged-Lepton Flavor Violation

Concentrating on rare muon processes, like µ → eγ µ → ee+ e− µ → e−conversion in nuclei

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Ever since it was established that µ → eν ν¯, people have searched for µ → eγ, which was thought to arise at one-loop, like this: ν

µ

γ

e

The fact that µ → eγ did not happen, led one to postulate that the two neutrino states produced in muon decay were distinct, and that µ → eγ, and other similar processes, were forbidden due to symmetries. To this date, these so-called individual lepton-flavor numbers seem to be conserved in the case of charged lepton processes, in spite of many decades of (so far) fruitless searching. . . March 14, 2012

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UL Branching Ratio (Conversion Probability)

Searches for Lepton Number Violation (µ and e) 10 10 10 10 10 10 10 10 10 10

-1 -3 -5 -7 -9

-11 -13 -15 -17

µ →eγ µ- N→ e- N µ+e-→ µ-e+ µ →eee KL → π+ µ e KL → µ e KL → π0 µ e

-19

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Year

[hep-ph/0109217] March 14, 2012

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SM Expectations? In the old SM, the rate for charged lepton flavor violating processes is trivial to predict. It vanishes because individual lepton-flavor number is conserved: • Nα (in) = Nα (out), for α = e, µ, τ . But individual lepton-flavor number are NOT conserved– ν oscillations! Hence, in the νSM (the old Standard Model plus operators that lead to neutrino masses) µ → eγ is allowed (along with all other charged lepton flavor violating processes). These are Flavor Changing Neutral Current processes, observed in the quark ¯ 0 , etc). sector (b → sγ, K 0 ↔ K Unfortunately, we do not know the νSM expectation for charged lepton flavor violating processes → we don’t know the νSM Lagrangian !

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One contribution known to be there: active neutrino loops (same as quark sector). In the case of charged leptons, the GIM suppression is very efficient. . .

e.g.: Br(µ → eγ) =

3α 32π

P 2 2 ∆m ∗ Uei M 21i < 10−54 i=2,3 Uµi W

[Uαi are the elements of the leptonic mixing matrix, ∆m21i ≡ m2i − m21 , i = 2, 3 are the neutrino mass-squared differences]

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MAX B(CLFV)

e.g.: SeeSaw Mechanism [minus “Theoretical Prejudice”] 10

τ→ µγ

-9

-10

10

τ→ µµµ -11

10

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µ→e conv in

-12

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Ti

µ→ eγ

-13

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µ→ eee -15

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arXiv:0706.1732 [hep-ph]

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The MEG Experiment

Liq. Xe Scintillation Detector

Liq. Xe Scintillation Detector

Thin Superconducting Coil Muon Beam

g

Stopping Target

e+

g

Timing Counter

e+

Drift Chamber

Drift Chamber

1m

W. Molzon, UC Irvine

March 14, 2012

NuFact 2006 - Status of the MEG Experiment

August 28, 2006

5

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⇑ Dominant Background

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Br(µ → eγ) < 2.4 × 10−12 (90% CL)

[MEG Coll. arXiv:1107.5547]

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µ+ → e+ e+ e− Backgrounds: – µ+ → e+ ννγ ∗ (→ e+ e− ) – accidentals (like µ → eγ) Handle: – vertexing, needs excellent tracking Yet to hit a wall. Proposal at PSI (?) [N. Berger at NuFact’11] March 14, 2012

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Independent from neutrino masses, there are strong theoretical reasons to believe that the expected rate for flavor changing violating processes is much, much larger than naive νSM predictions and that discovery is just around the corner. Due to the lack of SM “backgrounds,” searches for rare muon processes, including µ → eγ, µ → e+ e− e and µ + N → e + N (µ-e–conversion in nuclei) are considered ideal laboratories to probe effects of new physics at or even above the electroweak scale. Indeed, if there is new physics at the electroweak scale (as many theorists will have you believe) and if mixing in the lepton sector is large “everywhere” the question we need to address is quite different: Why haven’t we seen charged lepton flavor violation yet?

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Model Independent Considerations LCLFV =

mµ µ ¯ σ e F µν + (κ+1)Λ2 R µν L κ + (1+κ)Λ ¯L γµ eL 2µ

u ¯L γ µ uL

Λ (TeV)

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+ d¯L γ µ dL



B(µ→ e conv in 48Ti)>10-18

• µ → e-conv at 10−17 “guaranteed” deeper probe than µ → eγ at 10−14 .

10

4

B(µ→ e conv in 48Ti)>10-16

• We don’t think we can do µ → eγ better than 10−14 . µ → e-conv “only” way forward after MEG. B(µ→ eγ)>10-14

• If the LHC does not discover new states µ → e-conv among very few process that can B(µ→ eγ)>10-13

access 1000+ TeV new physics scale: tree-level new physics: κ  1,

1 Λ2



g 2 θeµ . 2 Mnew

10

3

EXCLUDED 10 March 14, 2012

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-1

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10 κ

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Other Example: µ → ee+ e− LCLFV =

mµ µ ¯ σ e F µν + (κ+1)Λ2 R µν L

Λ (TeV)

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-16

B(µ→ eee)>10

3000

κ + (1+κ)Λ ¯L γµ eL e¯γ µ e 2µ

B(µ→ eγ)>10-13 B(µ→ eee)>10-15

2000

• µ → eee-conv at 10−16 “guaranteed” deeper B(µ→ eee)>10-14

probe than µ → eγ at 10−14 . • µ → eee another way forward after MEG?

• If the LHC does not discover new states

1000 900 800 700 600 500

µ → eee among very few process that can 400

access 1,000+ TeV new physics scale: tree-level new physics: κ  1,

1 Λ2



g 2 θeµ . 2 Mnew

10

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EXCLUDED

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“Bread and Butter” SUSY plus High Energy Seesaw  







→ θe˜µ˜ ∼



  

Br(µ → eγ) '

α3 π 2 θ 2 4 e˜µ ˜ GF m ˜

∆m2e˜µ ˜ m ˜



, m ˜ 2 is a typical supersymmetric mass. θe˜µ˜ measures the “amount” of flavor violation.

For m ˜ around 1 TeV, θe˜µ˜ is severely constrained. Very big problem. “Natural” solution: θe˜µ˜ = 0

March 14, 2012

→ modified by quantum corrections.

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The Seesaw Mechanism αβ

MN 2

Nα Nβ + H.c., ⇒ N α gauge singlet fermions, L ⊃ −yiα L HN − αβ yiα dimensionless Yukawa couplings, MN (very large) mass parameters. i

α

At low energies, integrate out the “right-handed neutrinos” Nα : L⊃

−1 t yMN y ij



Li HLj H + O



1 2 MN

 + H.c.

y are not diagonal → right-handed neutrino loops generate non-zero ∆m2e˜µ˜

m2`˜L

 ij

MX 3m20 + A20 X ∗ (y) (y) ln , '− ki kj 8π 2 M Nk

X = Planck, GU T, etc

k

If this is indeed the case, CLFV would serve as another channel to probe neutrino Yukawa couplings, which are not directly accessible experimentally. Fundamentally important for “testing” the seesaw, leptogenesis, GUTs, etc March 14, 2012

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What are the neutrino Yukawa couplings → ansatz needed!

B(µ → eγ) × 1011

tan β = 10

title10

1000 CKM 007 000

100

SO(10) inspired model.

10 Now 1

remember B scales with y 2 .

y

0.1 0.01

MEG

2 [ln(M /M )]2 B(µ → eγ) ∝ MR R Pl

0.001 0.0001 1e-05 1e-06 1e-07 0

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800 x

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M1/2 (GeV) [Calibbi, Faccia, Masiero, Vempati, hep-ph/0605139]

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µ → e conversion is at least as sensitive as µ → eγ

B(µTi → eTi) × 1012

tan β = 10

title10

1000 CKM MNS

SO(10) inspired model.

100 10

Now

1

remember B scales with y 2 .

y

0.1

2 [ln(M /M )]2 B(µ → eγ) ∝ MR R Pl

0.01 0.001 1e-04 1e-05

PRIME

1e-06 1e-07 0

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800 x

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SUSY with R-parity Violation The MSSM Lagrangian contains several marginal operators which are allowed by all gauge interactions but violate baryon and lepton number. A subset of these (set λ00 to zero to prevent proton decay, and ignore bi-linear terms, which do not contribute as much to CLFV) is: L

=

c λijk (¯ νLi eLj e˜∗Rk + e¯Rk νLi e˜Lj + e¯Rk eLj ν˜Li )

+

jα λ0ijk VKM



λ0ijk

c ν¯Li dLα d˜∗Rk

u ¯cj eLi d˜∗Rk

+ d¯Rk νLi d˜Lα + d¯Rk dLα ν˜Li



+ d¯Rk eLi u ˜Lj + d¯Rk uLj e˜Li + h.c.,



The presence of different combinations of these terms leads to very distinct patterns for CLFV. Proves to be an excellent laboratory for probing all different possibilities. [AdG, Lola, Tobe, hep-ph/0008085]

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 4×10−4 Br(µ+ →e+ γ) Br(µ+ →e+ e− e+ )





=

R(µ →e in Ti (Al)) Br(µ+ →e+ e− e+ )

m2 1− ν˜2τ 2m e ˜R

2 ' 1 × 10−4

β

=

−5

2 (1)×10 β



5 6

+

m2ν˜τ 12m2e˜ R

µ+ → e+ e− e+ most promising channel! March 14, 2012

+ log

(β ∼ 1)

m2e m2ν˜ τ

2 +δ

' 2 (1) × 10−3 ,

[AdG, Lola, Tobe, hep-ph/0008085]

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Br(µ+ →e+ γ) Br(µ+ →e+ e− e+ )

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= 1.1 (md˜ = mc˜L = 300 GeV) R

R(µ− →e− in Ti (Al)) Br(µ+ →e+ e− e+ )

= 2 (1) × 105

µ − e-conversion “only hope”! March 14, 2012

[AdG, Lola, Tobe, hep-ph/0008085]

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Randall-Sundrum Model (fermions in the bulk) - dependency on UV-completion(?) - dependency on Yukawa couplings - “complementarity” between µ → eγ, µ − e conv

[Agashe, Blechman, Petriello, hep-ph/0606021] March 14, 2012

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Rate

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ε=0.003, Λ=1 TeV, (λ=0.54)

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τ→µγ

τ→µγ eγ µ→

µ-e conv

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-no ambiguity in y (neutrinos Dirac) -dependency on UV-completion

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10 -5 10 -5 – – ε=0.0003, Λ=1 TeV, (λ =0.17) ε=0.0003, Λ=10 TeV, (λ =1.7) 10 10 10 10 10 10 10 10

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What is This Really Good For? While specific models (see last slides) provide estimates for the rates for CLFV processes, the observation of one specific CLFV process cannot determine the underlying physics mechanism (this is always true when all you measure is the coefficient of an effective operator). Real strength lies in combinations of different measurements, including: • kinematical observables (e.g. angular distributions in µ → eee); • other CLFV channels; • neutrino oscillations; • measurements of g − 2 and EDMs; • collider searches for new, heavy states; • etc. March 14, 2012

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Vector 4-Fermion Interaction (Z) ∝ (¯ µγα e)(¯ q γ α q)

Vector 4-Fermion Interaction (γ) Dipole (∝ µ ¯σαβ eF αβ ) Scalar 4-Fermion Interaction ∝ (¯ µe)(¯ q q)

March 14, 2012

[Cirigliano, Kitano, Okada, Tuzon, 0904.0957] Intense Physics

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Model Independent Comparison Between g − 2 and CLFV: The dipole effective operators that mediate µ → eγ and contribute to aµ are virtually the same: mµ µν µ ¯σ µFµν Λ2

×

θeµ

mµ µν µ ¯σ eFµν Λ2

θeµ measures how much flavor is violated. θeµ = 1 in a flavor indifferent theory, θeµ = 0 in a theory where indiviadual lepton flavor number is exactly conserved. If θeµ ∼ 1, µ → eγ is a much more stringent probe of Λ. On the other hand, if the current discrepancy in aµ is due to new physics, θeµ  1 (θeµ < 10−4 ). [Hisano, Tobe, hep-ph/0102315] e.g., in SUSY models, Br(µ → eγ) ' 3 × 10−5



−9

10 δaµ

  ∆m2 2 e ˜µ ˜ 2 m ˜

Comparison restricted to dipole operator. If four-fermion operators are relevant, they will “only” enhance rate for CLFV with respect to expectations from g − 2.

March 14, 2012

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What we can learn from CLFV and other searches for new physics at the TeV scale (aµ and Colliders): g−2

CLFV

What Does it Mean?

YES

YES

New Physics at the TeV Scale; Some Flavor Violation

YES

NO

New Physics at the TeV Scale; Tiny Flavor Violation

NO

YES

New Physics Above TeV Scale; Some Flavor Violation – How Large?

NO

NO

No New Physics at the TeV Scale; CLFV only way forward?

Colliders

CLFV

What Does it Mean?

YES

YES

New Physics at the TeV Scale; Info on Flavor Sector!

YES

NO

New Physics at the TeV Scale; New Physics Very Flavor Blind. Why?

NO

YES

New Physics “Leptonic” or Above TeV Scale; Which one?

NO

NO

No New Physics at the TeV Scale; CLFV only way forward?

March 14, 2012

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What Will Happen in the Near Future . . . • Mu2e and COMET: µ → e-conversion at 10−16 . • g − 2 measurement a factor of 3–4 more precise. • Project X-like: µ → e-conversion at 10−18 (or precision studies?). • Project X-like: deeper probe of muon edm. • Muon Beams/Rings: µ → e-conversion at 10−20 ? Revisit rare muon decays (µ → eγ, µ → eee) with new idea?

March 14, 2012

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Summary and Conclusions • Low-energy muon processes constitute a powerful (often unique) probe of new physics around the electroweak scale, not unlike high-energy collider experiments (similar sensitivity to new physics energy scale). • Muon decay is the cleanest weak decay process (not as “messy” as nuclear beta decay...). It provides one of the “input” constants of the Standard Model (GF ), which is used as input for computing other electroweak observables. Precision studies of polarized muon decay are still very sensitive to New Physics. • Precision measurements of the anomalous magnetic moment of the muon are among the most stringent tests of the Standard Model. Understanding of the Standard Model expectations has settled somewhat, and an intriguing discrepancy (> 3 σ) remains? First evidence of new physics at the electroweak physics? Time will tell.

March 14, 2012

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• We know that charged lepton flavor violation must occur. Effects are, however, really tiny in the νSM (neutrino masses too small). • If there is new physics at the electroweak scale, there is every reason to believe that CLFV is well within the reach of next generation experiments. Indeed, it is fair to ask: ‘Why haven’t we seen it yet?’ • It is fundamental to probe all CLFV channels. While in many scenarios µ → eγ is the “largest” channel, there is no theorem that guarantees this (and there are many exceptions). • CLFV may be intimately related to new physics unveiled with the discovery of non-zero neutrino masses. It may play a fundamental role in our understanding of the seesaw mechanism, GUTs, the baryon-antibaryon asymmetry of the Universe. We won’t know for sure until we see it!

March 14, 2012

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March 14, 2012

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(From Talk by D. Bryman)

March 14, 2012

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New Physics: Exchange 10−4 (MW )−2 by Cnew (Mnew )−2 Intense Physics

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March 14, 2012

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March 14, 2012

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March 14, 2012

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March 14, 2012

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large data samples may teach us a lot . . . depending on where we are late in this decade March 14, 2012

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March 14, 2012

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KL → π 0 ν ν¯ has never been observed. “nothing in – nothing out”. Very hard experimentally!

goal of the KOTO experiment in J-PARC – around 50 events, assuming SM rate.

March 14, 2012

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March 14, 2012

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