Hints of New Physics in the Decay Σ+→pµ+µ−

E. Craig Dukes University of Virginia

HyperCP Collaboration

XL Rencontres de Moriond

Rencontres de Moriond HyperCP 1 HyperCP: Fermilab experiment searching for rare and forbidden charged hyperon decays

• Search for exotic sources of CP violation in Ξ−→Λπ−→pπ−π− decays • Precision measurement of hyperon decay parameters: – α, β, and γ decay parameters in Ξ−→Λπ− decays – α decay parameter in Ω±→ΛK± • Search for rare and forbidden charged kaon and hyperon decays – lepton-number violation: Ξ−→pµ−µ− –FCNC: K±→π±µ+µ− – ∆S > 1 decays: Ξ−→pπ−π−, Ω−→Λπ− – Σ+→pµ+µ−

Rencontres de Moriond HyperCP 2 New hyperon beam and high-rate spectrometer built

1.0

0.8

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Acceptance 0.4

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0.0 100 120 140 160 180 200 220 240 Momentum (GeV/c)

Charged Secondary Beam High-Rate Magnetic Spectrometer • 800 GeV protons on 2x2mm2 • 8 high-rate, narrow-pitch MWPCs target • left and right muon stations • mean momentum: 167 GeV/c • dimuon and single-muon triggers • rate: 10-15 MHz • very high-rate DAQ: 100,000 evts/s to • alternate +/- running tape

Rencontres de Moriond HyperCP 3 HyperCP yields

Rencontres de Moriond HyperCP 4 Motivation

In SM Σ+→pµ+µ− highly suppressed → leading diagrams FCNC and WR decays – – – W + + + m m m s d s u u u u,c,t W + u u p + u d p + s u p W u u u u u d • Hence sensitive to New Physics • Important: the phase space for New Physics at low mass scales has not been fully explored

–

X0 m+ s d + u u p u u

Rencontres de Moriond HyperCP 5

Removing kaon background

• Huge K+ background: ~0.5 billion reconstructed K+→π+π−π+ sample •In Σ+→pµ+µ− proton carries most momentum ⇒ require "hadron" momentum f = ≥ 0.68 hadron total Σ momentum

Decay Mode Branching Ratio ε(%) K+→π+π−π+ 5.6% 0.0

+ + − + −5 K →π π µ νµ 1.4×10 ~0.0 K+→π+µ+µ− 8.1×10−8 0.4

• Monte Carlo studies show K-decay background negligible

Rencontres de Moriond HyperCP 7 Three Σ+→pµ+µ− decays survive all cuts

Basic selection cuts Basic + fhadron selection cuts

7 events, 3 signal, 4 bkgd

• Observe 3 events with 1σ of the Σ mass (1189 MeV) • Backgrounds 20σ away from Σ mass

•fhadron cut gets rid of all but 7 events

Rencontres de Moriond HyperCP 8 Can these events be background?

• MC indicates backgrounds not a problem: but with ~1x1010 K+ decays non-gaussian tails can be a problem • Look at data: – Negative polarity data sample shows no events • about ½ size of positive polarity sample • Note: anti-Σ+ production down by ~10X – Single muon trigger sample 30X larger has more background, but no events below 1200 MeV

Rencontres de Moriond HyperCP 9 Can these events be photon conversions?

• Probability of a photon conversion in the vacuum pipe window ~ 10-7 • Monte-Carlo studies of K→π+π0, K→π+γγ, Σ+→pπ0, Σ+→pγ, with 100- 1,000 times the expected level show no background • Proton momentum not consistent with Σ+→pγ two-body decay • No evidence of much larger Σ+→pe+e− rate if photon conversions were a problem (γ→e+e− 105X γ→µ+µ−)

Rencontres de Moriond HyperCP 10 Extracting the branching ratio

• Since our acceptance is not perfect we need to know the form factors • Form factors cannot be calculated ab initio • Four form factors: a, b, c, d –aand b (at q2 = 0) come from WR decay Σ+→pγ + 2 2 Γ(Σ →γp ) ~ a + b 2Re(ab*) α = 2 2 a + b b(0) ⇒ = −0.46 ± 0.7 a(0) a(0) = 6.8 ± 0.2 MeV –cand d limited by on B(Σ+→pe+e-) < 7×10−6

+ µ µ+ − +10 −8 B(Σ → p ) = [13−8 ± 7]×10 (uniform decay) + µ + − +6.6 −8 B(Σ → p µ ) = []8.6−5.4 ± 5.5 ×10 (form factor) • smallest branching ratio ever measured for a baryon

Rencontres de Moriond HyperCP 11 What does theory say?

• Bergström, Safadi and Singer, ZPC 37, 281 (1988)

+ + − + −6 B(Σ →pe e ) ~ B(Σ →pγ)•ae ~ 10 B(Σ+→pµ+µ−) ≤ 1/100 B(Σ+→pe+e−) ~ 10−8

• Updated calculation by He, Tandean, and Valencia, PRD 72, 074003 (2005)

9.1×10−6 ≤ B(Σ+→pe+e−) ≤ 10.1×10−6 PDG: <7x10-6 1.6×10−8 ≤ B(Σ+→pµ+µ−) ≤ 9.0×10−8

• HyperCP result consistent with theory, albeit a bit high.

+ µ µ+ − +10 −8 B(Σ → p ) = [13−8 ± 7]×10 (uniform decay) + µ + − +6.6 −8 B(Σ → p µ ) = []8.6−5.4 ± 5.5 ×10 (form factor)

Rencontres de Moriond HyperCP 12 NothingUntil terribly you look exciting at the about µ+µ− massthis result

• The dimuon masses of all 3 events are within 1 MeV of each other! • This is the mass resolution of the HyperCP spectrometer • Suggests that the decay proceeds via an intermediate state, X0 µ µ Σ+ →pX0, X0 → + − 2 M 0 ( . . ) MeV/c X = 214 3± 0 5 + 0 0 µ+ − 2.4 −8 B(Σ →pX , X → µ ) = [3.1±1.9 ±1.5]×10

Rencontres de Moriond HyperCP 13 Can this be real?

• Is it a statistical fluctuation? – Probability of 3 events having µ+µ− mass within 1 MeV of each other anywhere in the kinematically allowed range is ~1% – Form factors can’t be fudged to increase that probability by much • Is it muonium? Not likely: it is 3.0 MeV

(6.0 σ) above 2mµ •Is it γ→ µ+µ−? Probability is negligible and if true we would see loads of events in the e+e− mode. • Is it the analysis or detector? We’ve looked hard, but we don’t see anything wrong. He, Tandean, Valencia PRD (2005)

Rencontres de Moriond HyperCP 14 What about Σ+→pe+e−?

• Much more difficult than Σ+→pµ+µ− – no electron identification – prescaled by 100X, although BR expected to be ~100X larger – WR decay background a problem: Σ+→pγ, γZ→ e+e− •Clear Σ+ peak • Most of the events appear to be Σ+→pe+e− , but Σ+→pγ, γZ→ e+e− background still being studied •No sign of X0, but we don’t expect to see it •e+e− distribution consistent with SM expectation

Rencontres de Moriond HyperCP 15 Suppose X0 is real

• Why wasn’t it seen before? • What properties does it have? – HyperCP can say little on this subject • know its mass • lifetime: not a resonance and not super long-lived • don’t know its spin • don’t know branching ratios: however X0→µ+µ− must be large • Is there any theoretical context for such a particle? • Where else can we look for it?

Rencontres de Moriond HyperCP 16 Kaon searches eliminate all but a parity-conserving pseudoscaler

• If either parity violating or scalar, HyperCP would have seen it in K+→π+µ+µ− at the 10-10 level • Vector possibility ruled out by + − KL→γµ µ : – KTeV found 9237 decays + − –B(KL→γµ µ ) = (3.62±0.04±0.08)×10−7 0 – No evidence of KL→γX , X0→µ+µ− • However: existing constraints on parity-conserving pseudoscalar weak

Rencontres de Moriond HyperCP 17 Who ordered that? Supersymmetry

• Sgoldstino: superpartner to the goldstino, the longitudinal component of the gravitino • Properties: Spin: 0, all other properties ill-determined: – Mass: 0 at tree level; obtains mass from Kähler potential, however expected to be light – Lifetime: can be long or short lived – Should be two: scalar (S) and pseudoscalar (P) – Can have flavor conserving and flavor violating interactions – Interactions with quarks may or may not conserve parity: however theoretical motivation for parity-conserving interaction – Branching ratio to dimuons can be large if light (< 2m ) “Parity conservation in sgoldstino interactions with quarks and π • Hyperonsgluons may a goodnot be place accidental… to searchIt is likelyfor parity-conserving that sgoldstino pseudoscalar sgoldstino A = 100 GeV A =1000 GeV interaction will conservel parity in supersymmetricl versions of √F = 1 TeV (SUSY “…if the sgoldstino is sufficiently light, the hyperon otherB(P models→γγ) designeddecays to into solve baryon91.3% the and strong sgoldstino CP problem are9.5% kinematically without breaking scale) introducing light axion.” B(P→µ+µ−) allowed and searches8.7% for these decays90.5% are very Mγγ ~100 GeV (order of Gorbunavsensitive and Rubakov,PRD to sgoldstino coupli 64,ngs 054008 in models (2001) with light B(P→e+e−) pseudoscalar0.001% sgoldstino and parity conservation.”0.01% photino mass) D.S. Gorbunov, Proc. Quarks-2004 cτ(cm) 0.02 0.003 Al: soft-mass term •B(Σ+→pX0) < 10−3 –10−6 (Gorbunov) Rencontres de Moriond HyperCP 18 Where to look for parity-conserving pseudoscalar

Note: Four-body kaon decay limits weak. K+→π+π0X0 < 10−12 X0→γγ, e+e−, µ+µ− 0 0 0 + − 0 −8 KL→π π X , π π X <10 0 0 0 + − 0 −11 KS→ π π X , π π X < 10 Only other hyperon mode Ω−→Ξ−X0 ~ 10−6 accessible e+e−→γX0 σ = 1pb – 5ab e+e−→e+e−X0 } D+→π+π0X0 B+→K+π0X0

Gorbunov and Rubakov, PRD 73, 035002 (2006)

Rencontres de Moriond HyperCP 19 There are more exotic explanations!

Diether and Inopin, physics/0601110

If these explanations are not exotic enough, please consult Rocky Kolb.

Rencontres de Moriond HyperCP 20 Where do we go from here?

• We have plumbed all the dimuon data there is at HyperCP • The dielectron analysis is ongoing, however preliminary analysis shows nothing unexpected • We are searching for Ω−→Ξ−X0, X0→µ+µ−, but we expect at best only one or two events • It would be easy to mount a new experiment and take ~10X more data: unfortunately Tevatron no longer available for fixed-target physics at Fermilab • Other experiments should take up the challenge: is this another crack in the Standard Model or another unexplained experimental anomaly? • Note: now published, H.K. Park et al., Phys. Rev. Lett. 94, 021801 (2005)

Rencontres de Moriond HyperCP 21 Backup Slides

Rencontres de Moriond HyperCP 22 Systematic Errors

Rencontres de Moriond HyperCP 23 Searches for light boson

• Many experiments have searched for a light boson • Few searches for a short-lived boson of mass ~200 MeV/c2

Rencontres de Moriond HyperCP 24