Low Energy Tests of the Standard Model and Beyond

Low Energy Tests of the Standard Model and Beyond Jens Erler Departamento de Física Teórica Instituto de Física Universidad Nacional Autónoma de México (IF-UNAM) MAMI and Beyond Schloß Waldthausen March 30 April 3, 2009

Plan Introduction: probes of the SM and beyond Conservation laws: B, L, charged lepton flavor Symmetry violations: hadronic flavor, CP, P Lepton scattering: elastic ep, Møller, e-dis, ν-dis Lepton properties: lifetimes, decay, g 2, ν-mass Conclusions

Introduction Probes of the SM and beyond

Low energy probes ν: scattering, oscillations, magnetic moments muonic atoms, muonium: LFV e: polarization asymmetries, g 2, EDM μ: lifetime, decay parameters, g 2, LFV, EDM τ: lifetime, BRs, spectral functions, LFV atoms, ions, molecules, solids: PNC, EDMs

Hadronic and nuclear probes Mesons: weak decays, mixings cc, bb : resonance parameters, production X-section p: lifetime, EDM n: lifetime, decay parameters, EDM, n-n oscillation ²H: EDM ³H: ordinary β-decay nuclei (10 < A< 74): superallowed 0+ 0+ β-decays heavy nuclei: ν ββ-decay

High energy probes t: pair decays, single (EW) production X-section W: mass, width, BRs, anomalous gauge couplings Z: lineshape parameters, BRs, asymmetries H: collider searches

Conservation laws B, L, charged lepton flavor

Baryon number violation Allowed (kind of) in the SM as instanton process, such as ³He e+ μ+ ν (τ), but unobservably small. τ(p e+ π ) > 1.6 10 a (Super-Kamiokande) Γ m = C 16π (g 360 MeV Λ) < (6.1 10 ) Λ > 2.2 10 GeV (for C = g = 1) C 30 in minimal SUSY-SU(5), but excluded through τ(p K+ ν ) > 2.3 10 a (Murayama, Pierce 2001). τ(n n ) > 4.1 a (Soudan 2) Γ/m < (5.9 10 > C 256π g (360 MeV Λ) Λ 250 GeV

Lepton number violation R(μ Ti e+ Ca) = Γ(μ Ti e+ Ca) Γ(μ Ti ν Sc) < 3.6 10 (SINDRUM II) Λ > 100 TeV B(K+ π μ+ e+) < 5 10 (BNL) Λ > 50 TeV observation of ν ββ-decay Majorana neutrinos τ( Ge Se + 2e ) > 1.9 10 a (Heidelberg- Moscow) (11 kg) mᵦᵦ 0.35 (1 ± 0.5) ev or Λ g 3.2 ± 0.3 TeV (e.g. heavy Majorana neutrino) (100 kg, 1 t) detectors mᵦᵦ ~ 0.1 (0.04) ev covering degenerate (probing inverted) ν-masses.

Charged lepton flavor violation Effects induced by ν loops unobservably small. B(K μ e) < 4.7 10 (BNL) Λ > 450 TeV B(μ 3e) < 1.0 10 (SINDRUM) Λ > 250 TeV B(μ e γ) < 1.2 10 (MEGA) Λ > 240 TeV R(μ Ti e Ti) = Γ(μ Ti e Ti) Γ(μ Ti ν Sc) < 6.1 10 (SINDRUM II) Λ > 280 TeV SUSY-GUTs, right-handed νs, non-universal Z's,... ΔL = 2: B(μ+ e μ e+) (PSI) Λ > 5.3 TeV

CLFV: future MEG (running): μ e γ ~ 2 10 (Λ 700 TeV) PSI & MUSIC (studied): μ 3e 10 (Λ 1 PeV) Mu2e & COMET (proposed): μ e (Al) ~ 6 10 PRISM & Project X (planned): μ e (Ti) ~ 10 (Λ 3 PeV and Λ 8 PeV) 1/200 < B(μ e γ) R(μ Ti e Ti) < 200 (dipole operator contact interaction) diagnostics after discovery: target dependence (μ e), detailed kinematics (μ 3e), polarizations

Symmetry violations Hadronic flavor, CP, P

Flavor changing neutral current B(K+ π+ ν ν ) = (1.73 ± 1.1) 10 (7 events at BNL-E787/949) Λ 76 TeV (in SM, loop and strongly CKM suppressed) R(e/μ) = Γ[π+ e ν (γ)] Γ[π+ μ ν (γ)] = (1.2310 ± 0.0037) 10 (PSI & TRIUMF) Λ 820 TeV (much more than a universality test) ΔS = 2: [m(bᴴ) m(bᴸ)] [m(bᴴ) + m(bᴸ)] = (3.160 ± 0.031) 10 (BaBar, Belle, CDF, D0, LEP) Λ 13 PeV, but theory error Λ 3 PeV

FCNC: future CERN-NA62: B(K+ π+ ν ν ) ~ 10 KEK-391a & J-PARC: B(K π ν ν ) ~ 2 10 KOPIO (concept for Project X or J-PARC): both B(K π ν ν ) ~ 10 SES (Λ 800 TeV) both extremely clean theoretically, especially the CPV nothing in, nothing out ; K+ (K ) useful for modulus (Im) of V(td)V(ts)*: superior to V(ub) PIENU & PEN: R(e/μ) ~ 5 10 (Λ 2 PeV) CERN: R(e/μ) for K+ ~ 10

CKM first row unitarity superallowed 0+ 0+ β-decays (Hardy, Towner): V(ud) = 0.97424(8)(10)(18) = 0.97424 ± 0.00022 π β-decay: V(ud) = 0.9748 ± 0.0025 (PIBETA) K decays: V(us) = 0.22478 ± 0.00124 (KLOE) using f+(0) = 0.9644(49) (RBC/UKQCD) K decays: V(us) V(ud) = 0.23216 ± 0.00145 (KLOE) using f(k) f(π) = 1.189(7) (HP/UKQCD) V(ud) ² + V(us) ² + V(ub) ² = 1.0000 ± 0.0006 Λ 10 TeV

CKM first column unitarity σ(ν N μ μ+ X) σ(ν N μ X) (ν ν ) σ(ν valence-d μ c) V(cd) ² B(c μ+ ν ) V(cd) = 0.230 ± 0.011 (CDHS, CCFR, CHARM II) using B(c μ+ ν ) = 0.0873(52) (FNAL-E53I, CHORUS) V(ud) ² + V(cd) ² + V(td) ² = 1.0021 ± 0.0051 Λ 3.4 TeV Leptoquarks, W*(KK), heavy quark mixing, Z'-loops, new physics contributions to μ-decay ( Fermi constant)

CP violation ε [m(kᴸ) m(kˢ)] [2 m(k⁰)] = (7.801 ± 0.042) 10 (PDG) Λ 460 PeV, but theory error Λ 140 PeV ε' Λ 800 PeV, even assuming 100% SM theory uncertainty (cancellations between EW and QCD penguins) new physics CP problem in general more serious than flavor problem

Electric dipole moments CKM-CPV too small to produce BAU or EDMs. relativistic effects in paramagnetic atoms: d(tl) < 9.6 10 e cm (Berkeley) d(e) < 1.6 10 e cm Λ > 56 TeV (if tree level induced; for loops divide by ~ 2π) nuclear Schiff moments in diamagnetic atoms: d(hg) = (1.06 ± 0.63) 10 e cm (Seattle) and d(hg) < 2.1 10 e cm θ < 1.5 10 d(n) < 2.9 10 e cm (ILL) θ < 10

EDMs: future eedm: laser-cooled atoms, polar molecules, molecular ions and solids expect breakthroughs. PSI, J-PARC & FNAL: μedm ~ 10 e cm (30 TeV) Argon: d(ra) ~ 10 e cm (θ ~ 10 ) PSI, ILL, LANL & SNS: nedm ~ 10 e cm SREC: (p)dedm ~ (3 )10 e cm (θ ~ 10 ) 3 10 θ e cm d(n) d(p) 3 d(d) SUSY: d(d) 20 d(n) 200 d(e) 10 e cm

Atomic parity violation Nuclear spin-independent PV sensitive to q-vector e -axial-vector couplings (C₁ᵢ, weak charges A³) spin-dependent PV probes q-axial e -vector couplings (C₂ᵢ A²) & anapole moment ( A most precise (only) measurement of weak charge (nuclear anapole moment) in ¹³³Cs (Boulder) interpretation needs very good understanding of atomic structure; most precise calculation Qᵂ(¹³³Cs) = 73.17 ± 0.29 (exp.) ± 0.20 (theory) (Derevianko 2008) Λ 4.8 TeV

APV: future Seattle: single trapped Ba+(Ra+) ~ ±0.35% (Cs-like) Dunford, Holt 2007: D (H) slow meta-stable beams ~ ±0.3% (from free electron lasers?) TRIUMF: cold trapped Fr (Cs-like but effect 18 times larger weak charge, anapole moment) Berkeley (ongoing): Yb isotope ratios (DeMille 95); Yb and Yb have I 0 (anapole moment, C₂ᵢ); 5 even isotopes (max. ΔN = 8 neutron density) Yale: diatomic molecules (anapole moment, C₂ᵢ)

(plot by Sidney Cahn)

Lepton scattering Elastic ep, Møller, e-dis, ν-dis

Elastic ep scattering Qweak (JLab): E = 1.165 GeV, Q² 0.026 GeV², P 85 ± 1 % extrapolate Qweak point + previous data to Q²= 0 ΔQᵂ(p) = ± 0.0029 Δ sin²θᵂ = ± 0.00072 Λ 4.6 TeV (Ramsey-Musolf, JE 2003) hadronic uncertainty in higher orders (γz-box) begin of installation: late October (6 months) end of data taking (6 months): May 14, 2012

Polarized Møller scattering SLAC E-158: E = 45 & 48 GeV, P 89 ± 4 % Q² m E 0.026 GeV² (high energy, low Q²) Aᴿᴸ = (1.31 ± 0.14 ± 0.10) 10 ⁷ Qᵂ(e) SM tree level: Qᵂ(e) g²(r) g²(l) 1 + 4 sin²θᵂ( Q²) 0.045 Qᵂ(e) = 0.0403 ± 0.0053 sin²θᵂ(z-mass) = 0.2330 ± 0.0014 (Czarnecki, Marciano 1996) or Λ 3.4 TeV

1000 all data: 90% CL 500 M H [GeV] 200 100 50 1! contours: A LR (had.) [SLC] A FB (b) [LEP] 20 10 M W low-energy m t 95% CL excluded 140 150 160 170 180 190 m t [GeV]

Møller scattering: future e2epv (JLab): E = 11 GeV, Q² 0.0064 GeV², P 85 ± 0.5 % Aᴿᴸ 3.4 10 ⁸ (1 ± 0.023) ΔQᵂ = ± 0.0011 Δ sin²θᵂ = ± 0.00029 or Λ 7.5 TeV compare with SLD: ± 0.00029, best LEP: ± 0.00028 complementary to Tevatron (eeqq-couplings), LEP 2 [g²(r) g²(l), g²(rl)] and eedm (C P) compositeness, SUSY, Z's, doubly charged scalars

Parity-violating DIS Prescott et al. (1978) experiment established SM E08-011 (JLab-Hall A before 12 GeV upgrade): E = 6 GeV, Q² = 1.1 (1.9) GeV² PV-DIS (JLab after upgrade): using baseline equipment (Hall C) or build new device (Hall A) improve SLAC (global fit) by factor 54 (17) PDFs: higher twist (CSV) go with Q² (x) (2 C¹ᵘ C¹ᵈ) 0.84 (2 C²ᵘ C²ᵈ) ~ 0.0049 (Λ 2.5 TeV)

E = 6.6 (11) GeV, P = 85% (from Hall A proposal)

νn and ν N-DIS NuTeV: 2.0 σ deviation (in flux), effect of Kᵉ BR? was 2.7 σ before inclusion of dx x (S S ) = 0.0020 ± 0.0014 (NuTeV now agrees with CTEQ) QED radiative corrections (Diener, Dittmaier, Hollik 2004), but not yet included by NuTeV CSV due to quark model and QED splitting effects can each remove 1 σ; phenomenological CSV PDFs can remove/double the effect (MRST) nuclear effects: different for NC and CC; 20% of effect, both signs possible (Brodsky, Schmidt, Yang)

0.250 0.245 SM current future A FB (lep) [Tevatron] sin 2 ^! W (!" 0.240 0.235 Moller [SLAC] APV(Cs) Moller [JLab] "-DIS antiscreening Qweak [JLab] screening A LR (had) [SLC] 0.230 PV-DIS [JLab] A FB (b) [LEP] 0.225 0.001 0.01 0.1 1 10 100 1000! [GeV]

Lepton properties Lifetimes, decay, g 2, ν-mass

μ lifetime and Fermi constant τ(μ) = 2.197034 ± 0.000018 μs (μlan, FAST) G(F) = (1.166367 ± 0.000005) 10 GeV or Λ 246.2209(5) GeV Δ 120 TeV (but can t eat the cake and have it, too) need next best G(F) from Z-mass and weak mixing angle (indirect) Λ 11 TeV (W-mass: Λ 6 TeV) amounts to an analysis of oblique parameters like S,T, U (Peskin, Takeuchi 1990) or ε₁, ε₂, ε₃ (Altarelli, Barbieri 1990)

τ lifetime and strong coupling τ(τ), B(τ e ν ν ) and B(τ μ ν ν ) αˢ OPE applicable, incredibly shrinking error, suppression of duality violations, spectral functions for SM test one again needs a 2nd opinion: Z-width, σ⁰(hadrons), Γ(Z l+ l ) Γ(Z hadrons) significant downward shift: αˢ = 0.1185 ± 0.0016 Baikov, Chetyrkin, Kühn (2008): 4-loop PQCD Maltman (2008): dimension 4, 6, 8 terms of OPE Jamin, Beneke (2008): FOPT CIPT

μ and τ decays μ-decay: Michel and Sirlin parameters ρ = 0.75080 ± 0.00047 (TWIST) Λ 11 TeV final precision for ρ ~ ± 0.00027 (Λ 13 TeV) wrong μ handedness, LR symmetric models τ-decay: spectral functions (in tandem with e+ e ) constrain higher dimensional operators in OPE quark-hadron duality & isospin (CVC) violations running α (QED) & weak mixing angle, g 2

Muon g 2 BNL E-821: 2.7-3.4 σ (3 10 ⁹) deviation (in flux) SUSY (tanβ 1, light superpartners, sign(μ) > 0) 2-loop vacuum polarization: dispersion calculation based on CMD 2 & SND (e+e hadrons) and KLOE (radiative ϕ returns) which are inconsistent with BaBar (R(s) from radiative Υ(4S) returns) and Belle (τ ν π π & CVC): 3.4 1.7 σ after BaBar 3-loop γ γ: no first principles calculation π⁰ + VMD: (1.16 ± 0.40) 10 ⁹ (Nyffeler 2009) free quarks: < 1.59 10 ⁹ (Toledo, JE 2006)

Muon g 2: future FiNALe: ~ 1.5 10 (Λ 8.6 TeV) CMD 2 & SND: factor 2-3 improvement KLOE: normalize to muon R(s) BaBar: τ ν π π Theory (task): CVC and γ γ

ν-mass atmospheric νs: Δm² 0.05 ev (Super-Kamiokande, K2K, MINOS) Λ 1.2 10 GeV (see-saw scale or scale of effective dimension 5 operator) ν ββ-decay: angular distribution 1 k cosθ may discriminate between (Ali, Borisov, Zhuridov 2006) long-distance ν-mass (k = 1) and some short-distance models (e.g., with righthanded currents)

Conclusions

Conclusions Low energy tests give constraints which are very complementary to high energy colliders. Depending on which symmetries the physics beyond the SM violates, extremely high energy scales are testable. Some subfields at the verge of revolutions. Intensity/precision frontier strong future player.

Backup slides

Current and future μ physics μlan, FAST: μ-lifetime Fermi constant < 1 ppm TRIUMF Michel and Sirlin μ-decay parameters MuCap, MuSun: μ p (d) n (n) ν gᴾ, LECs MEG: BR(μ+ e+ γ) 10 ¹³ (3 10⁸ μ/s) Mu2e: μ N e N 10 ¹ 10¹¹ μ/s), Λ 3 PeV FiNALe: g 2 1.5 10 ¹ Λ/g 1 TeV in loops μ-edm (E-821, PSI, FNAL): 10 ¹ 10 ²², 10 ² e cm μ collider: s ~2-3 TeV (ν radiation); needs 10¹³ μ/s

!"#$#%&'%(&)*+,$"#%&-+'./"+0+%$.&1"+&2++(+( JLab Qweak SLAC E158 PRL 95, 081601 (2005)

Effective e γ⁵eq q couplings Young, Carlini, Thomas, Roche (2007)

Normalized ep-asymmetries