New Physics effect on the Top-Yukawa coupling

New Physics effect on the Top-Yukawa coupling

KOJI TSUMURA (KEK)in collaboration with Shinya Kanemura (U-Toyama), Koichi Ma

tsuda (Tsinghua-U), Daisuke Nomura (KEK)

LCWS07 and ILC07DESY, Hamburg, May 30- June 3

This talk is based on PRD74,076007(2006)

LCWS07 May 30-June 3 KOJI TSUMURA 2

Plan of talk

• Introduction– Top-Yukawa coupling at a LC

• Effective Theory– Dimension-six operators as a new physics– Constraints on dim.6 ops.

• New physics effect on the Top-Yukawa coupling at a LC

• Summary


Introduction


Why Top-Yukawa coupling• Why the Yukawa coupling ?

– Gauge interactions are well examined.– To understand the mass generation mechanism. It is necessary to measure mass and Yukawa coupling separately.

• Why the top ?– Large Yt is essentially important at future colliders.

– Why the top exceptionally heavy ?– Are the top and EWSB related ?

　 Top-quark might have new physics !?


Top-Yukawa coupling at a LC• For lighter Higgs boson (SM or SUSY like scenario)

– ee -> ttH associate production

• For heavier or intermediate Higgs masses

– If theory has relatively heavy Higgs bosons. In the non-SM, non-SUSY such as LH, xD, TC, etc., WW-fusion can be an useful probe.

T. Han, et. al. PRD61, 015006 (2000)

Kanemura, Nomura, KT PRD74,076007(2006)


Top-Yukawa coupling at a LC• For lighter Higgs boson (SM or SUSY like scenario)

– ee -> ttH associate production


– WBF ee -> nu nu tt

– We discuss the new physics effect on the top-Yukawa coupling in the wide range of Higgs boson mass.


Effective theory description

Dimension-six operators as a new physics


Effective theory• Eff. Lagrangian below the new physics scale

– The non-SM interactions are characterized by dim.6 gauge invariant operators at leading order.

– There are so many dim.6 operators. We introduce these dim.6 ops. for 3rd generation quarks. •Bottom quark operators are strongly constrained by Z→bb.

Buchmuller et. al in NPB268, 621 (1986)


Dimension-six top-quark operators

Buchmuller et. al in NPB268, 621 (1986)


Origin of dim.6 operators

•MSSM PRD69,115007 Feng, Li, Maalampi


• Direct search– No experimental bound for .– can be constrained by Tevatron.

for

Experimental limits on dim.6 ops.

K. i. Hikasa et al 　 PRD58, 114003 (1998)


Experimental limits• Precision data

– can give oblique corrections. It can be allowed in the SM-like situation with heavier Higgs bosons.

– Ex.

G. J. Gounaris et al PRD 52, 451 (1995)S. Kanemura, D. Nomura. KT PRD74, 076007(2006)


• Amplitudes

– Imposing unitarity @

– Considering 2-body scattering channels (hh, WLW

L, ZLZL, and t anti-t), chirality and color factors.

Perturbative unitarityG. J. Gounaris et al Z. Phys. C 76, 333 (1997)

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

We will use above sample values of dim.6 couplings.


• Operators t1 and Dt only contribute to the Top-Yukawa coupling


Effect of dim.6 on Higgs decay

• Eff. Top-Yukawa

– is restricted by mt .– Dim.6 couplings are only constrained by unitarity.

• Decay width– At the tree level, top-pair production can

be modified.– Loop induced decays can be enhanced.FIG. 1: The top pair production via W boson fusion


C t1 0 ¡ 16¼3p

2¤v + 16¼

3p

2¤v 0 0

CDt 0 0 0 +10:2 ¡ 6:2








jCt1j ·16¼

3p

2

µ¤v

¶; (8)

¡ 6:2 · CD t · 10:2: (9)








6



New physics effect on the Top-Yukawa coupling at a LC


ee -> ttH Associate production• For lighter Higgs boson

– ee -> ttH associate production can be a useful probe to constrain the new physics effect on dim.6 Top-Higgs interaction.

PRD61,015006 Han et al


ee -> ttH associate production

• The X sections of the process ee -> ttH as a function of CM energy for .

• The dashed curves are the SM predictions.

• New physics effect can be easily observed in the ee -> ttH process.



ee -> ttH associate production

• mH dependence of the X sections of the process ee -> ttH with operators

and .• When mH becomes large, the X se

ctions and its deviation from the SM are quickly decrease.


How to study the top-Yukawa coupling for relatively heavy mH ?


Top-Yukawa coupling at a LC


– If theory has relatively heavy Higgs bosons. In the non-SM, non-SUSY such as LH, xD, TC, etc., WW-fusion can be an useful probe.


In this talk, we examine the possibility to study the new physics effect on the top-Yukawa coupling in the W-boson fusion process for large mH.



W boson fusion (WBF)– At the high energy LC, WBF is an important Higgs production channel.

– A few thousands of top-pair events produced via WBF.

– BGs have been studied. Godfrey, Zhu PRD72,074011Kanemura, Nomura, KT PRD74,076007(2006)

The X sections for WBF sub-process are calculated in the SM, longitudinally polarized W-boson gives dominant contribution

mH =500GeV


with dim.6 ops.

• Cutoff scale is set to be 1TeV.• Dim.6 couplings can change the cross sections by a factor. • Since Higgs decay width grow wider, X sections can be enhance

d not only the sub-process energy equal to mH pole.

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 ESS

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

SM

SM



C t1 0 ¡ 16¼3p

2¤v + 16¼

3p

2¤v 0 0

CDt 0 0 0 +10:2 ¡ 6:2








jCt1j ·16¼

3p

2

µ¤v

¶; (8)

¡ 6:2 · CD t · 10:2: (9)








6


mH =500GeV


Check (by using ET)

• Our calculations can be checked by ET.

– S-matrix for WL scattering is equivalent to those for NG-boson up to m/E. Dotted curves indicate the process .

SM

SM



• Solid , dotted • We only impose cut .• The total cross section can be enhanced by factor

of 2 in the range .

• The effects of become large for heavier Higgs compare to those of .

Effect of dim.6 on tot.X section in WBF

SMSM



C t1 0 ¡ 16¼3p

2¤v + 16¼

3p

2¤v 0 0

CDt 0 0 0 +10:2 ¡ 6:2








jCt1j ·16¼

3p

2

µ¤v

¶; (8)

¡ 6:2 · CD t · 10:2: (9)








6



Effect of dim.6 on tot.X section in WBF

SMSM



C t1 0 ¡ 16¼3p

2¤v + 16¼

3p

2¤v 0 0

CDt 0 0 0 +10:2 ¡ 6:2








jCt1j ·16¼

3p

2

µ¤v

¶; (8)

¡ 6:2 · CD t · 10:2: (9)








6


At the ILC with , several hundred events are expected. Statistical error is less than 10 %. Therefore the effect of dim.6 couplings can be observed.


Summary


• We discuss the W-fusion with the non-SM Yt which are characterized by dim.6 operators.

• They are constrained by EXP. data and unitarity.– Our calculations have been checked by ET.– Dim.6 couplings can enhance cross sections.

Summary

Conclusion

Dim.6 couplings can enhance cross sections, the effect can be observed in the WBF for heavier Higgs bosons.


Thank you for your listening !!


Feynman rules• Feynman rules for dimension-six operators.


Origin of dim.6 ops.PRD69,115007 Feng, Li, Maalampi


Origin of dim.6 ops.PRD69,115007 Feng, Li, Maalampi


Higgs decay branching ratios• Higgs decay branching ratio in the SM


Higgs decay branching ratios with dim.6 coupling


F. Larios, T. Tait, and C. P. Yuan, Phys. Rev. D 57, 3106 (1998)

J. Alcaraz and E. Ruiz Morales,

Phys. Rev. Lett. 86, 3726 (2001)

W boson fusion (WBF)– At the high energy LC, W-fusion is an important probe.

– A few thousands of top-pair events produced via vector boson fusion.

– BGs have been studied.

J. Alcaraz and E. Ruiz Morales,

Phys. Rev. Lett. 86, 3726 (2001)


Effective W approximation (EWA)• W-bosons are treated as a parton which are emitted

by initial electron and positron.

• At the leading order, parton distributions for WL consists the process 　　　 with 　 approximation .– The validity of EWA will

be shown by using the package CalcHEP.




s in







when m2H = ¡ q2 ' (600GeV)2.






and LanHEP[30].




9

S. Dawson, Nucl. Phys. B249, 42 (1985)

http://link.aip.org/link/?&l_creator=getabs-normal&l_dir=FWD&l_rel=CITES&from_key=PRVDAQ000074000007076007000001&from_keyType=CVIPS&from_loc=AIP&to_j=NUPBBO&to_v=249&to_p=42&to_loc=DOI&to_url=http%3A%2F%2Fdx.doi.org%2F10.1016%2F0550-3213%2885%2990038-0

http://link.aip.org/link/?&l_creator=getabs-normal&l_dir=FWD&l_rel=CITES&from_key=PRVDAQ000074000007076007000001&from_keyType=CVIPS&from_loc=AIP&to_j=NUPBBO&to_v=249&to_p=42&to_loc=DOI&to_url=http%3A%2F%2Fdx.doi.org%2F10.1016%2F0550-3213%2885%2990038-0


• 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.

At the ILC with , several hundred events are expected. Statistical error is less than 10%.

The validity of EWA

SM

A. Pukhov, hep-ph/0412191


Amplitudes with dim.6 couplings for WW scattering




s in







when m2H = ¡ q2 ' (600GeV)2.






and LanHEP[30].




9


Amplitudes with dim.6 couplings (NG-bosons)

FIG. 6: Feynman diagrams for the subprocess ! ¡ ! + ! t¹t in the model with the dimension-six

operators Ot1 and OD t.

As seen from Eq. (13), the operator Ot1 represents the shift of the SM top-Yukawa

coupling, whileOD t givesitsmomentumdependence. Thee®ect of OD t enhancesthee®ective

Yukawa coupling asp

s grows until the cuto®scale ¤. It turns out that this momentum

dependence of the e®ective Yukawa coupling due to OD t in the Higgs boson mediation is

replaced by the Higgs boson mass dependence due to the gauge cancellation mechanism.

The invariant amplitude of the subprocess is obtained as

M W W ! tt = M W W ! ttH + M W W ! tt

b + M W W ! ttZ + M W W ! tt

° : (17)

Calculation of the amplitudecan be tested by using theequivalenceof the longitudinally

polarized weak boson (W §L ) and the corresponding Nambu-Goldstoneboson (! § ) for

ps À

mW [33]. In the Feynman gauge, the diagrams for the process ! ¡ ! + ! t¹t are shown in

Fig. 6, and each diagram is calculated as

M ! ¡ ! + ! t¹t£ (2¼)3

p2p0

q2p00 = ¡

Ct1

¤2

vp

2¹utvt; (18)

M ! ¡ ! + ! t¹tH (2¼)3

p2p0

q2p00 =

m2H =v

s ¡ m2H + imH ¡ H

ye®t (s;¤)

p2

¹utvt; (19)

M ! ¡ ! + ! t¹t° (2¼)3

p2p0

q2p00 = ¡

Qte2

s¹utiP=vt; (20)

M ! ¡ ! + ! t¹tZ (2¼)3

p2p0

q2p00 = ¡

g2Z (1¡ 2sinµ2

W )4(s ¡ m2

Z )¹ut

µiP=(Vt + A t°5) +

CD t

¤2

v

2p

2K ¢P

¶vt;

(21)

M ! ¡ ! + ! t¹tb (2¼)3

p2p0

q2p00 = ¡

1u ¡ m2

b

µySM

t ¡CD t

¤2p¢k0

¶ 2

¹utPL i(p=¡ k0=)vt; (22)

where momenta p (p0) and k (k0) are de ned in a similar way to the case of W ¡ W+ ! t¹t.

The invariant amplitude is obtained as

M ! ! ! tt = M ! ! ! tt£ + M ! ! ! tt

H + M ! ! ! tt° + M ! ! ! tt

Z + M ! ! ! ttb : (23)

11


• Cross sections for the sub-process

– Dim.6 coupling can give negative contributions.

Sub-process X section vs dim.6 couplings




s in







when m2H = ¡ q2 ' (600GeV)2.






and LanHEP[30].




9


Equivalence theorem• Our calculations can be checked by equivalence theorem. – S-matrix for longitudinally polarized W boson scattering is equivalent to those for NG-boson up to mass/energy.

•BRS identity

•Equivalence between longitudinal pol. and scalar pol. at high energies.


Unitarity cancellation

• In the SM, the amplitude for WW scattering does not divergent at high energies due to unitarity cancellation.

• The effects of dimension-six operator rapidly grow higher energy.

• However, the SM-like unitarity cancellation can take place, the total cross section is stabilized up to the cutoff scale.


Tot.X section vs dim.6 couplings• Total cross section for the process


– WBF process with the non-SM Yt which

are characterized by dim.6 operators is discussed.– They are constrained by EXP. data and unitarity.

• Dim.6 couplings can enhance cross sections, the effect can be observed in the WBF.

New Physics effect on the Top-Yukawa coupling

SM

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New Physics effect on the Top-Yukawa coupling