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New Physics search via WW-fusion at the ILC
Koji TSUMURA (Osaka Univ. → KEK after April)in collaboration with S. Kanemura & K. Matsuda
KEK Theory Meeting on Particle Physics Phenomenology 2007 Mar. 1-3
KEK-PH 07 Mar. 1-3 Koji TSUMURA 2/15
Introduction
• 4-fermi interaction has been tested in collision & decays.• ee -> WW has been well examined @ LEP by using helicity an
alysis.
• For Higgs boson & heavy fermions, we would like to study vector boson fusion (WW-fusion) process.– Higgs boson strongly couples to heavy particles.
Kanemura, Nomura, Tsumura, PRD74:076007,2006Larios et.al. hep-ph/9709316Asakawa, Hagiwara, Eur.Phys.J.C31:351,2003Grzadkowski et.al. JHEP 0511:029,2005Cho, Hagiwara et.al. PRD73:054002,2006
Gaemews et.al. Z.Phys.C1:259,1979 Hagiwara et.al. Nucl.Phys.B282:253,1987 Hagiwara et.al. NPB496,66,1996
KEK-PH 07 Mar. 1-3 Koji TSUMURA 3/15
New Physics search via top-Higgs interaction
– For lighter Higgs boson (SUSY like scenario)• ee -> ttH associate production
– For heavier or intermediate Higgs boson masses
• If theory has (relatively) heavy Higgs, WW-fusion can be an useful probe.
(Effective theory approach, extra Higgs, Little Higgs, Extra-D, Top Color, etc.)
T. Han, et. al. PRD61, 015006 (2000)
KEK-PH 07 Mar. 1-3 Koji TSUMURA 4/15
Effective theory approach
– Below the new physics scale , the non-SM int. is characterized by higher dimension operators.
– The coupling strength can be calculated in each model.– ex. MSSM Feng, Li, Maalampi PRD69,115007
– ex. Extra Higgs
KEK-PH 07 Mar. 1-3 Koji TSUMURA 5/15
– Complete set of gauge invariant dim.6 ops. Has been discussed.
Buchmuller et. al in NPB268, 621 (1986)
• 4-fermi operators • Scalar only (6 scalar, 4 scalar + 2 derivative)• Scalar & vector operators• 2-fermi operators (Yukawa + 2 scalar)• 2-fermi operators (Yukawa + 2 derivative [2 vector] )… so many operators !!
– We introduce these dim.6 ops. for 3rd generation quarks. • Bottom quark operators are strongly constrained by Z→bb.
Dimension-six operators
KEK-PH 07 Mar. 1-3 Koji TSUMURA 6/15
Experimental limits
– Direct search• No experimental bound for .• There are no stringent bounds for
by vector boson exchange processes at LEP and Tevatron.
ex. for
– Precision data• can give oblique corrections.
Hikasa et. al. PRD58, 114003 (1998)
Gounaris et. al. PRD52, 451 (1995)
has no linear contribution.
Ot1 : no experimental boundOt3 : weaker bound from oblique correctionODt : smaller ⊿ρ compare to t2, tWΦ, tBΦ
In this talk, we concentrate on three dim.6 operators Ot1: direct correction for top-Yukawa
ODt: correction for top-Yukawa including derivativesOt3: right-handed vector interaction
KEK-PH 07 Mar. 1-3 Koji TSUMURA 7/15
Unitarity bounds– Tree level unitarity for dim.6 ops. Has been discussed. Gounaris et. al. in Z. Phys. C76, 333
(1997).
• Imposing unitarity @ • Considering 2-body scattering channels (hh, WLWL, ZLZL,
hZL and t anti-t), then we obtained
KEK-PH 07 Mar. 1-3 Koji TSUMURA 8/15
Effects of dimension-six coupling– Effective top-Yukawa
– Decay width for Higgs boson Kanemura Nomura Tsumura PRD74, 076007 (2006) • For , non-SM effect (only ) can be observed i
n the top-pair production .• For lighter Higgs mass, loop induced decays
can be enhanced.• For , we can not reach non-SM effect.
(main ) FIG. 1: The top pair production via W boson fusion
Ci Set A Set B Set C Set D Set E
C t1 0 ¡ 16¼3p
2¤v + 16¼
3p
2¤v 0 0
CDt 0 0 0 +10:2 ¡ 6:2
TABLE I : Sets of the dimension-six couplings we used for the analyses.
dimension-six operators Oi can beconstrained theoretically by using theidea of partial wave
unitarity[15]. Due to thestructureof a dimension-six operator, the two-body elastic scatter-
ing amplitudes is proportional to the square of thescattering energy, so that the coe±cient
becomes strong at someenergy scale, and violate tree-level unitarity. T he unitarity bounds
for thecoe±cients Ci=¤2 areobtained by setting the scaleof unitarity violation to beabove
¤. T he bounds for Ct1 and CD t are evaluated as
jCt1j ·16¼
3p
2
µ¤v
¶; (8)
¡ 6:2 · CD t · 10:2: (9)
These results are almost the same as those in Ref. [13].
The value of the anomalous coupling Ct1 is free from the constraint from current exper-
imental data[16, 24], because it only a®ects the genuine interaction between the top quark
and the Higgs boson which has not been measured yet. T herefore, only the theoretical
consideration such as perturbativeunitarity is important to constrain this operator. On the
other hand, CD t turns out to receive strong experimental limits from the electroweak rho
parameter result[16, 25, 26], since theoperator OD t changes the interaction of the top quark
6
KEK-PH 07 Mar. 1-3 Koji TSUMURA 9/15
– Solid , dotted – The non-SM (t1,Dt) effect can be
significant under the unitarity bounds.
WW-fusion @ ILC Kanemura Nomura Tsumura PRD 74, 076007 (2006)
SMSM
The non-SM (t1,Dt) effect can be significant under the unitarity bounds.
How to extract more information ?
Smaller dim.6 coupling ?Smaller Higgs mass ?
Much operators ?Separate each operator ?
KEK-PH 07 Mar. 1-3 Koji TSUMURA 10/15
Helicity amplitude for WW-fusion
– Amplitudes are calculated which respect to W-boson helicity and t-quark spin.
• To obtain further information, we consider top-quark spin correlations.
• By using W-boson helicity, each amp. can be checked by BRS sym.
• In this talk, we concentrate on the WW-fusion sub-process.FIG. 4: Feynman diagrams for the subprocess W ¡ W + ! t¹t in the SM.
FIG. 5: T he helicity cross sections for W ¡¸ W +
¹ ! t¹t as a function of the collision energyp
s in
the SM, where ¸ (¹ ) is the helicity of the incoming W ¡ (W +) boson. T he mass mH of the Higgs
boson is set to be 500 GeV.
OD t. The results for the decay branching ratios are shown in Fig. 3 for Set A, Set B, ¢¢¢,
and Set E. We note that in Set E a cancellation of the branching ratio of H ! t¹t can be
seen between theSM contribution and that from OD t around mH » 600 GeV. T his happens
since the ¯rst term and the third term in the right-hand side of Eq. (11) cancel each other
when m2H = ¡ q2 ' (600GeV)2.
I I I . SU B P ROC E SS
Weherestudy thecross section for thesubprocess W ¡ W + ! t¹t[27]. By using the results
in this section, we evaluate the cross section of the full process e¡ e+ ! W ¡ W +º ¹º ! t¹tº ¹º
in thethee®ectiveW approximation (EWA)[28] in Sec. IV , and compareit to thenumerical
results of calculation of the full matrix elements by the full useof thepackages CalcHEP[29]
and LanHEP[30].
In theSM, Feynman diagrams for thesubprocess areshown in Fig. 4. Cross sections ¾SM¸ ¹
for thehelicity amplitudes of W ¡¸ W+
¹ ! t¹t with helicity sets (¸, ¹ ) areshown as a function
9
KEK-PH 07 Mar. 1-3 Koji TSUMURA 11/15
WW-fusion in the SM
LL polarized WW is dominant.
Effect of top-Yukawa
Other polarization sets
KEK-PH 07 Mar. 1-3 Koji TSUMURA 12/15
WW-fusion with Ot1
Higgs width become wide
Not changed !!
Enhanced by the effect of effective top-Yukawa
KEK-PH 07 Mar. 1-3 Koji TSUMURA 13/15
WW-fusion with ODt
Enhanced by the effect of effective top-Yukawa
Enhancement from the t-channel process Direct effect of Dt
Energy dependence differ from t1
KEK-PH 07 Mar. 1-3 Koji TSUMURA 14/15
WW-fusion with Ot3
little enhancement through t-channel
Strongly modified vector int. in right-handed vector current
KEK-PH 07 Mar. 1-3 Koji TSUMURA 15/15
Summary
– New Physics effect can be seen in WW-fusion.– dim.6 operators can be distinguished by using helicity metho
d (top-spin correlation)• We concentrate on the WW-fusion sub-process.• We should calculate spin correlation for the full-process.
• We should estimate detectable
size of dim.6 coupling.
– Issues• Smaller values of dim.6 coupling.
(not only t1,Dt,t3 but also t2, tWΦ,tBΦ)• Lighter Higgs
KEK-PH 07 Mar. 1-3 Koji TSUMURA 16/15
WW-fusion @ ILC Kanemura Nomura Tsumura PRD 74, 076007 (2006)
– Dotted curves are calculated by using the package CalcHEP.• The EWA results agree with those of CalcHEP in about
20-30 % error for heavier Higgs boson.
SM