From the Planck Scale to the Electroweak Scale, La Londe-les-Maures, France, 11 - 16 May 2001

Athanasios Dedes

University of Bonn, Germany

Can the Higgs sector contribute

significantly to the

muon anomalous magnetic moment?

In collaboration with: H. E. Haber, hep-ph/0102297, JHEP to appear

We show :

1. A light CP-even Higgs boson with m_{h} ∼ O(10) GeV could explain the recent BNL measurement of the muon anomalous magnetic moment

2. Framework : General CP-conserving two-Higgs-doublet extension of the Standard Model with no tree-level flavor-changing neutral Higgs couplings

3. Significant contribution to muon g − 2 without violating known experimental constraints only if the hZZ coupling (approximately) vanishes and M_{Υ} < ∼ m_{h} < ∼ 2m_{B}.

Can the Higgs sector contribute significantly to the muon anomalous magnetic moment? 1

• Based on Davier-Höcker calculation for the Hadronic contributions to the muon g − 2, BNL reports a 2.6σ deviation from the SM

There are four possible interpretations of this discrepancy :

• a statistical fluctuation with 0.9% probability.

• something is “wrong” with the experiment

• something is “wrong” with the theoretical analysis of the hadronic contribution to the muon anomalous magnetic moment.

• the by far most exciting possibility:

there is “New Physics” BSM

215 × 10^{−11} < ∼ δa_{μ}^{NP} < ∼ 637 × 10^{−11} @90% CL

• δa_{μ}^{NP} is positive

• δa_{μ}^{NP} is of the same order of the EW contributions, δa_{μ}^{NP} ∝ \frac{G_{F} m_{μ}^{2}}{4π^{2}\sqrt{2}}

• Why not from the Higgs sector ?

Standard model (SM)

δa_{μ}^{h} ∝ \frac{G_{F}m_{μ}^{2}}{4π^{2}\sqrt{2}}(\frac{m_{μ}^{2}}{m_{h}^{2}} )

suppressed since m_{h} > ∼ 113.5 GeV

University of Bonn  1  Athanasios Dedes

Can the Higgs sector contribute significantly to the muon anomalous magnetic moment? 2

Two Higgs Doublet Model (II) [2HDM(II)] :

The enhancement from the Higgs sector to a_{μ} arises from two sources :

{h, A} − μ^{+} − μ^{−} ∝ tan β ⇒ δa_{μ}^{h,A} ∝ tan^{2} β
H^{−} − μ^{+} − ν ∝ tan β ⇒ δa_{μ}^{H^{±}} ∝ tan^{2} β

and

h − Z − Z ∝ sin(β − α) ≃ 0

then m_{h} can be as small as ∼ 10 GeV.

Can the Higgs sector contribute significantly to the muon anomalous magnetic moment? 3

2HDM(II) Higgs boson corrections to a_{μ}

μ h, H, A μ  μ μ γ  μ H^{−} ν γ H^{−} μ

Non-decoupling limit: sin(β − α) = 0

δa_{μ}^{Higgs} = δa_{μ}^{h} + δa_{μ}^{H} + δa_{μ}^{A} + δa_{μ}^{H^{±}}

≃ \frac{G_{F}m_{μ}^{2}}{4π^{2}\sqrt{2}} tan^{2} β\{\frac{m_{μ}^{2}}{m_{h}^{2}} [ln (\frac{m_{h}^{2}}{m_{μ}^{2}} ) − \frac{7}{6}] − \frac{m_{μ}^{2}}{m_{A}^{2}} [ln (\frac{m_{A}^{2}}{m_{μ}^{2}} ) − \frac{11}{6}] − \frac{m_{μ}^{2}}{6m_{H^{±}}^{2}} \} .

√ δa_{μ}^{H} can be neglected since it does not give a contribution proportional to tan β

√ A and H^{±} exchange contribute a negative value to δa_{μ}^{NP}.

√ In order to explain the BNL g − 2 we need positive corrections. We take m_{A} and m_{H^{±}} large, > ∼ 100 GeV.

√ If δa_{μ}^{NP} is to be a consequence of the Higgs sector, it must be entirely due to the contribution of the light CP-even Higgs boson.

Can the Higgs sector contribute significantly to the muon anomalous magnetic moment? 4

Therefore :

δa_{μ}^{Higgs} ≃ δa_{μ}^{h} ≃ \frac{G_{F}m_{μ}^{2}}{4π^{2}\sqrt{2}} (\frac{m_{μ}^{2}}{m_{h}^{2}} ) tan^{2} β[ ln (\frac{m_{h}^{2}}{m_{μ}^{2}} ) − \frac{7}{6}] .

A light Higgs boson with a mass of around 10 GeV and with tan β = 35 gives δa_{μ}^{Higgs} ≃ 280 × 10^{−11}, which is within the 90% CL allowed range for δa_{μ}^{NP}.

Decoupling limit: cos(β − α) = 0

√ The couplings of the light Higgs boson, h, are (nearly) identical to those of the SM Higgs boson : m_{h} > ∼ 113.5 GeV.

√ The H couplings to down-type fermion pairs are enhanced by tan β

√ For : cos(β − α) = 0 and m_{H} = m_{A} = m_{H^{±}}

δa_{μ}^{Higgs} ≃ \frac{G_{F}m_{μ}^{2}}{4π^{2}\sqrt{2}} (\frac{m_{μ}^{2}}{m_{A}^{2}} ) tan^{2} β[\frac{1}{2} − (\frac{2m_{μ}^{2}}{m_{A}^{2}} ) ln (\frac{m_{A}^{2}}{m_{μ}^{2}} )] .

√ For 100 GeV < m_{A} < 1000 GeV, and 30 < tan β < 100, the Higgs sector contribution to a_{μ} ranges from about 5 × 10^{−12} to 5 × 10^{−14}, which is three to five orders of magnitude below what is needed to explain the BNL measurement of a_{μ}.

Results

m_{Υ} < ∼ m_{h} < ∼ 2m_{B} , sin(β − α) ≃ 0 , 30 < ∼ tan β < ∼ 35 .

CESR constraints on the light m_{h}

• An experimental search for Υ → hγ by the CUSB Collaboration at CESR found no candidates.

• In addition to the non-relativistic, tree-level prediction there are :

• O(α_{s}) hard QCD corrections

• relativistic corrections to the non-relativistic treatment of the bb̄ bound state

• bound state threshold corrections

Standard Model: m_{h} < ∼ 5—7 GeV can be ruled out at 95% CL but no precise upper limit due to the theoretical uncertainties

2HDM : Γ(Υ → hγ) is enhanced by a factor of tan^{2} β

√ For values of tan β > ∼ 10, the CUSB data can reliably rule out Higgs masses up to about 8 GeV.

√ For large tan β ≃ 30 values, the tan^{2} β factor should dwarf the theoretical uncertainties!

m_{h} > ∼ m_{Υ}

[See red region in the previous figure]

LEP constraints on the light m_{h}

• A second bound on m_{h} can be derived from the nonobservation of Higgs bosons at LEP via the process e^{+}e^{−} → hff̄ (f = b, τ).

From J. Kurowska, O. Grajek and P. Zalewski [DELPHI Collaboration], CERN-OPEN-99-385.

Similar for m_{h}

From J.B. de Vivie and P. Janot [ALEPH Collaboration], PA13-027 contribution to the International Conference on High Energy Physics, Warsaw, Poland, 25–31 July 1996.

Can the Higgs sector contribute significantly to the muon anomalous magnetic moment? 9

• Other constraints :

• the one-loop process Z → hγ

• precision EW observables

→ weaker bounds on m_{h} − tan β than CESR+LEP ones

One noteworthy consequence of m_{h} ∼ 10 GeV

• the possibility of mixing between the h and the 0^{++} bb̄ bound states χ_{b0}(1P) and χ_{b0}(2P)

\frac{Γ(χ_{b0} → τ^{+}τ^{−})}{Γ(χ_{b0} → hadrons)} ≃ \frac{2.5 × 10^{−7} GeV^{2}}{(m_{χ} − m_{h})^{2}} tan^{4} β

√ Due to the large tan^{4} β enhancement, the predicted branching ratio for χ_{b0} → τ^{+}τ^{−} can be substantial.

√ Particle Data Group provides no data on possible decay modes of the χ_{b0} other than the radiative decays, χ_{b0} → Υγ, Υ′γ.

Final Results and Conclusions

• Combined CESR+LEP+BNL(DH) in 2HDM(II):

• m_{Υ} < ∼ m_{h} < ∼ 2m_{B} ,
• sin(β − α) ≃ 0 ,
• 30 < ∼ tan β < ∼ 35 .

• In addition, H, A and H^{±} must be sufficiently heavy to satisfy the LEP experimental constraints :

√ m_{H} > ∼ 113.5 GeV
√ m_{A} > ∼ 80 GeV
√ m_{H^{±}} > ∼ 78.7 GeV

These results can be confirmed or ruled out by :

• a more complete analysis by the LEP Collaborations of their data in search of e^{+}e^{−} → hff̄ (f = b or τ)

• further improvement of the BNL measurement of the muon anomalous magnetic moment a_{μ}

• further improvement of the theoretical calculations on the hadronic contributions to the muon anomalous magnetic moment.