QCD Effects in High-Energy Processes

C.S. Li and S.H. ZhuPeking UniversityJune 2005, Beijing

In collaboration with: S. Godfrey, W. Hollik, C.S. Huang, R. J. Oakes & C.P. Yuan

With contributions from Y. Gao, L.G. Jin, Q. Li, J.J. Liu, L.L. Yang

1. Introduction

2. QCD effects in Higgs physics

3. QCD effects in SUSY

4. QCD effects in top physics

5. Factorization & re-summation

6. Summary

Outline

QCD effects at high energy scale (perturbative region) are important in testing QCD & searching new physics beyond the SM.

Evaluating QCD effects are complicated at high energy scale due to: infrared & UV singularities, multiple final states, multiple loops, multiple scales (PT distribution, new particle etc.),

Recent progress on QCD, for examples

• QCD effects in particles decay & production of SM (Higgs, Top) and/or new physics (e.g. SUSY)

• Resummation techniques

(1) Introduction

•MHV

•AP splitting function at 3-loop,

•NNLO QCD di-lepton rapidity distribution of

Drell-Yan process

•NLO background

•Etc.

Is there fundamental scalar field in Nature?

Is electro-weak (EW) symmetry really broken by Higgs vacuum expectation value (VEV)?

2HDM, 3HDM, Triplet, SUSY Higgs, Little Higgs, Fat Higgs…?

QCD effects are important to answer above questions because they will affect Higgs production and decay.

Higgs physics is certainly the primary goal of next generation colliders.

(2) QCD effects in Higgs physics

Decay of SM Higgs

SM Higgs Production at Hadron Colliders

•Recent reviews by A. Djouadi, hep-ph/0412238, 0503172

LHC

Search of SM Higgs at Hadron Colliders

QCD corrections to H->

H.Q.Zheng, D.D.Wu, Phys. Rev. D 42, (1990) 3760

A.Djouadi, M.Spira, J,J,van der Bij, P.M.W.Zerwas,

Phys.Lett. B257 (1991) 187

S.Dawson, R.P.Kauffman, Phys.Rev. D47 (1993) 1264 A.Djouadi, M.Spira, P.M.W.Zerwas, Phys.Lett. B311 (1993) 255-260K.Melnikov,O.I.Yakovlev Phys.Lett. B312 (1993) 179-183M.Inoue, R.Najima, T.Oka, J.Saito, Mod.Phys.LettA9(1994)1189

M.Steinhauser hep-ph/9612395

J.Fleischer, O.V.Tarasov, V.O.Tarasov, Phys.Lett. B584 (2004) 294-297

Inclusive cross section for gg->H

The history of QCD corrections to this process is long.

14 years ago

NLO QCD corrections to gg->H are found to be large

A.Djouadi, M.Spira, P.M.Zerwas Phys.Lett.B264 (1991) 440

S.Dawson Nucl.Phys.B359 (1991) 283

D.Graudenz, M.Spira, P.M.Zerwas, Phys.Rev.Lett, 70 (1993) 1372

M.Spira, A.Djouadi, D.Graudenz, P.M.Zerwas, Phys.Lett.B318 (1993) 347

M.Spira, A.Djouadi, D.Graudenz, P.M.Zerwas, Nucl.Phys.B453 (1995) 17

NNLO QCD corrections to gg->H (effective Lagrangian method)

*Two-loop corrections to H-g-g vertexR.V.Harlander, Phys.Lett.B492 (2000) 74*Soft-plus-virtual gluon correctionsS.Catani, D.de.Florian, M.Grazzini, JHEP 0105 (2001) 025R.V.Harlander,W.B.Kilgore,Phys.Rev.D64 (2001) 013015 *Two-to-three body processes

R.V.Harlander, W.B.Kilgore, Phys.Rev.Lett.88 (2002) 201801

C.Anastasiou, K.Melnikov, Nucl.Phys.B646 (2002) 220

V.Ravindran, J.Smith, W.L.Van Neerven, Nucl.Phys.B665 (2003) 325

V.Ravindran, J.Smith, W.L.van Neerven, Pramana 62 (2004) 683

*NNLL Catani et al., Laenen et al., vogelsang et al. see the Resummation part in this talk

Taken from V.Ravindran et al., hep-ph/0405263

NLO QCD corrections to gg->H+1jet+X (in effective Lagrangian method )

D.de.Florian, M.Grazzini, Z.Kunszt, Phys.Rev.Lett.82 (1999)5209

S.Catani, D.de Florian, M.Grazzini,JHEP 0201 (2002) 015

V.Ravindran, J.Smith, W.L.Van Neerven, Nucl.Phys.B634

(2002) 247Christopher J.Glosser, Carl R.Schmidt, JHEP 0212 (2002) 016

NLO QCD correction to gg->diphoton

(background to gg->H->diphoton) Z.Bern, L.J.Dixon, C.Schmidt

Phys.Rev.D66 (2002) 074018

Associated production of Higgs with top pairs(NLO)

W.Beenakker, S.Dittmaier, M.Kramer, B.Plumper, M.Spira,

P.M.Zerwas

Nucl.Phys.B653 (2003) 151 Phys.Rev.Lett.87 (2001) 201805

S. Dawson, C. Jackson, L.H. Orr, L. Reina, D. Wackeroth Phys.Rev.D68 (2003) 034022

Tevatron LHC

W.Beenakker etal., Phys.Rev.Lett.87 (2001) 201805

The relevant Yukawa coupling can be large in SUSY models

bg->bh at LHC

C.S. Huang & S.H. Zhu, PRD60:075012,1999 F. Maltoni, Z. Sullivan, S. Willenbrock, Phys.Rev. D67 (2003) 093005 S.Dawson etc., Phys.Rev.Lett. 94 (2005) 031802

bb h

In collinear limit

d/dt ~1/t

From the figure, the collinear limit is about

After integration

The factorization should be about

ln( / 4 )h bm m

/ 4hm

/ 4ht m

Exclusive Higgs Boson Production with bottom quarks pairs at Hadron Colliders(SM and SUSY Higgs boson)(NLO)

S.Dawson, C.Jackson, L.H.orr, L.Reina, D.Wackeroth Phys.Rev. D69 (2004) 074027

QCD Corrections to Jet Correlations in Weak Boson FusionT.Figy,D.Zeppenfeld, Phys.Lett. B591 (2004) 297 Phys.Rev. D68 (2003) 073005; T.Figy, C.Oleari, D.Zeppenfeld

Phys.Rev. D68 (2003) 073005

SM Higgs Production at ILC

Taken from

A.Bartl, S.Hesselbach hep-ph/0404178

R.D.Heuer et al., hep-ph/0106315

NLO QCD Corrections to e+e-tth

QCD Corrections to Associated Higgs Boson-Heavy Quark Production, S.Dawson, L.Reina

Phys.Rev. D59 (1999) 054012S. Dittmaier, M. Krämer, Y. Liao, M. Spira, P.M. Zerwas, PLB441 (1998) 383

NLO QCD corrections to

Chen Hui,Ma Wen-Gan,Zhang Ren-you,Zhou Pei-Jun, Hou Hong-Sheng,Sun Yan-Bin

Nucl.Phys. B683 (2004) 196-218

tth

QCD and SUSY QCD correction to H->tb.

A.Mendez, A.Pomarol, Phys.Lett.B252 (1990) 461

C.S.Li, R.J.Oakes, Phys. Rev. D 43 (1991) 855

C.S.Li, J.M.Yang, Phys.Lett.B315(1993) 367

Heinz Konig, Mod. Phys. Lett. A10 (1995) 1113

A. Bartl, H. Eberl, K. Hidaka, T. Kon, W. Majerotto, Y. Yamada, Phys.Lett.B378:167-174,1996

MSSM Higgs Decay

SUSY-QCD decoupling properties in H-> t b M. Herrero, S. Penaranda, D.Temes, Phys.Rev. D64 (2001) 115003

QCD and SUSY QCD correction to t-> H+ b.

C.S.Li, T.C.Yuan, Phys.Rev.D42:3088-3092,1990, Erratum-ibid.D47:2156,1993

J. Liu,Y.P.Yao, Int.J.Mod.Phys.A6(1991)4925; Phys.Rev.D46:5196-5199,1992

B.Q.Hu, C.S.Li, J.M.Yang, Chin.Phys.Lett.10:329-332,1993

A. Czarnecki, S.Davison, Phys.Rev.D47:3063-3064,1993

QCD and SUSY QCD correction to H+->stop sbottom .

A.Bartl, H.Eberl, K.Hidaka, T.Kon, W.Majerotto, Y.YamadaPhys.Lett. B373 (1996) 117

Improved SUSY QCD corrections to Higgs decay into quark or squark pairH. Eberl, K. Hidaka, S. Kraml, W. Majerotto, Y. YamadaPhys.Rev. D62 (2000) 055006

QCD and SUSY-QCD corrections to the Three-Body Decay of the Charged Higgs BosonXiao-Jun Bi, Yuan-Ben Dai, Xiao-Yuan Qi,

Phys.Rev. D61 (2000) 015002

SUSY-QCD corrections to the MSSM hbb vertex in the decoupling limit

Howard E. Haber, Maria J. Herrero, Heather E. Logan, Siannah Penaranda, Stefano Rigolin, David Temes

Phys.Rev.D63 (2001) 055004

MSSM Higgs Production at Hadron Colliders

(Recent review by Djouadi, hep-ph/0503173 )

NNLO QCD corrections to pp->(pseudo) scalar Higgs boson

R.V.Harlander, W.B.Kilgore, JHEP 0210 (2002) 017

V.Ravindran,J.Smith,W.L.Van Neerven, Nucl.Phys.B665 (2003) 325

C.Anastasiou, K.Melnikov, Phys.Rev.D67 (2003) 037501

B.Field,J.Smith,M.E.Teieda-Yeomans,W.L.Van.Neerven

Phys.Lett. B551 (2003) 137

Effects of SUSY-QCD in hadronic Higgs production at NNLOR.V.Harlander, M.SteinhauserPhys.Rev. D68 (2003) 111701

NLO QCD corrections to Higgs+1 high PT bottom quark production

Stefan Dittmaier, Michael Krämer, Michael Spira

Phys.Rev. D70 (2004) 074010

J. Campbell, R.K. Ellis, F. Maltoni, S. Willenbrock

Phys.Rev. D67 (2003) 095002 J. Campbell, S. Dawson, S. Dittmaier, C. Jackson, M. Kramer, F. Maltoni, L. Reina, M. Spira, D. Wackeroth, S. Willenbrock

hep-ph/0405302SUSY-QCD corrections to gb->bh

Junjie Cao, Guangping Gao, Robert J. Oakes, Jin Min Yang

Phys.Rev. D68 (2003) 075012

NLO QCD corrections to Higgs+2 high PT bottom quark production

Stefan Dittmaier, Michael Krämer, Michael Spira

Phys.Rev. D70 (2004) 074010

S. Dawson, C.B. Jackson, L. Reina, D. Wackeroth

Phys.Rev. D69 (2004) 074027

NLO QCD corrections to gb->tH-

 Shou-Hua Zhu Phys.Rev. D67 (2003) 075006,hep-ph/0112109

T.Plehn Phys.Rev. D67 (2003) 014018, hep-ph/0206121

E Berger, T Han, J Jiang, T Plehn, hep-ph/0312286

NLO QCD corrections to bb->WH

Wolfgang Hollik, Shou-hua Zhu

Phys.Rev. D65 (2002) 075015

SUSY QCD corrections to gb->tH-

G. Gao ,G. Lu Z. Xiong, J.M.Yang

Phys.Rev. D66 (2002) 015007 

SH Zhu, Phys.Rev. D67 (2003) 075006,hep-ph/0112109

NLO QCD corrections to neutral Higgs pair production

Li Gang Jin, Chong Sheng Li, Qiang Li, Jian Jun Liu, Robert J. Oakes

Phys.Rev. D71 (2005) 095004

NLO QCD corrections to

Hou Hong-Sheng, Ma Wen-Gan, Zhang Ren-You, Jiang Yi, Han Liang, Xing Li-RongPhys.Rev. D71 (2005) 075014

0bb A Z NLO QCD corrections to

Qiang Li, Chong Sheng Li, Jian Jun Liu, Li Gang Jin, C.-P.Yuan

hep-ph/0501070

bb H H

Qiang Li, Chong Sheng Li, Jian Jun Liu, Li Gang Jin, C.-P.Yuan, hep-ph/0501070

MSSM Higgs Production at ILC

Taken from

A.Bartl, S.Hesselbach hep-ph/0404178

A.Djouadi,Montpellier, hep-ph/0205248

Taken from S. Dittmaier, M. Krämer, Y. Liao, M. Spira, P.M. Zerwas Phys.Lett. B478 (2000) 247

NLO QCD Corrections to e+etth( and bbH)

S. Dittmaier, M. Krämer, Y. Liao, M. Spira, P.M. ZerwasPhys.Lett. B478 (2000) 24

Shou-hua Zhu, hep-ph/0212273

Petra Häfliger, Michael Spira, hep-ph/0501164

Wu Peng, Ma Wen-Gan, Hou Hong-Sheng, Zhang Ren-You, Han Liang, Jiang Yi, hep-ph/0505086

NLO QCD corrections to

Bernd A. Kniehl, Fantina Madricardo, Matthias Steinhauser

Phys.Rev. D66 (2002) 054016

e e H tb

In a sense, MSSM is Standard Model of new physics beyond SM

Many advantages: solving gauge hierarchy problem, GUT, dark matter…

Is SUSY the real symmetry at TeV scale? Could be answered at future colliders?

QCD effects are important, especially for colored particle decay and production, and could be essential to distinguish SUSY breaking scenarios.

(3) QCD effects in SUSY

Sample spectra for SUSY particles for SUGRA, GMSB and AMSB scenarios.

hep-ph/0106315

The reach of the Tevatron, the LHC, and a 0.5 and 1 TeV LC for SUSY discovery.

A. Belyaev, hep-ph/0410385

• squark

• gluino

NLO QCD corrections to SUSY particle decays

243 (1998) PLB419 Bartl A.

510 '~,~

6975 (1997) PRD55 Djouadi A. 175; (1996) PLB386 Kraml S.

1020 ~',~

115007 (1999) PRD59 Bartl A. 5860; (1998) PRD57 Arhrib A.

2040 '~,//~

349 (1997) ZPC75159; (1996) PLB378 Beenakker W.

5030 ~~

0

0

000

et al.

%%~--WqZq

et al.et al.

%%~-qq

et al.et al.

%%~-HqAHhq

et al.

%%~gqq

349 (1997) ZPC75159; (1996) PLB378 Beenakker W.

1010 ~/~~

et al.

%%~-qqqqg

Hadron colliders (including the NLO QCD corrections)

- squarks,gluinos

- top-squark pairs

- gaugino pairs, slepton pairs

- gluino and gaugino

51 (1997) 492 NPB163; (1995) 69 ZPC2905; (1995) 74 PRL r W.Beenakke

~~,~~,~~,~~/

et al.

gqggqqqqpppp

3 (1998) 515 NPB r W.Beenakke

~~/

et al.

ttpppp

3780 (1999) 83 PRL r W.Beenakke5871; (1998) 57 PRD Baer H.

~~/~~

/

et al.et al.

llpppp

(E) 099901 (2003) 67 PRD

095014; (2000) 62 PRD 165; (1999) 459 PLB Berger E.L.

~~/

et al.

gpppp

- top-squark and chargino

- R-parity violating processes

L.G. Jin, C.S. Li & J.J. Liu, PLB 561 (2003) 135, EPJC30 (2003) 77

pp t

1 1

1

/ through

T. Plehn, PLB 488 (2000) 359

/

A. Alves PLB 558 (2003) 165

/ through /

L.L. Yang. C.S. Li & J.J. Liu, to be submitted to PRD

pp pp t t b bl

pp pp tl

et al.

pp pp l l v vl l l

Some typical results

M. Spira, hep-ph/0211145

M. Krämer, hep-ph/9809259

L.G. Jin, C.S. Li & J.J. Liu, EPJC30 (2003) 77

~~tpp

QCD effects can reach 20-30%.

Generally, the QCD corrections are large and positive, increasing the total cross sections by 10-90%. The inclusion of the NLO corrections reduces the LO scale dependence by a factor 3-4 and reaches a typical level of ~10-15% which serves as an estimate of the remaining theoretical uncertainty.

M. Spira, hep-ph/0211145

Linear collider (including the NLO QCD corrections) - squark pairs

073 (2004) 0404 JHEP Arhrib A.242; (2004) 591 PLB Kovarik K.

:scorrection loop-one complete

481 (1996) 472 NPB Eberl H. 1404; (1995) 52 PRD Arhrib A.

~~

et al.et al.

et al.et al.

qqee

055009 (2005) 71 PRD RongLi Xing

:scorrection loop-one complete

15 (1998) 515 NPB Chang C.H.

~~

et al.

et al.

qq

At linear colliders, in general, the QCD corrections are positive and dominant over other ones at the low colliding energy (e.g. 500-1000 GeV).

Is top really special just because of its mass at EW scale and the heaviest one among known particles?

Top with huge mass has saved SM, otherwise theoretical prediction are not consistent to precision data at LEP and SLC.

Top also brought troubles to dynamical EW symmetry breaking mechanisms (Technicolor, top-see-saw, Little Higgs, Higgsless models…)

QCD effects are important in testing SM or distinguishing new physics: SM or SUSY, models of dynamical symmetry breaking, and so on.

(4) QCD effects in top physics

• M. Jezabek,J.H. Kuhn, Nucl.Phys.B314(1989)1• A. Czarnecki, Phys.Lett.B252(1990)467• C.S.Li, R.J.Oakes, T.C.Yuan,

Phys.Rev.D43(1991)3759 • C.F.Qiao, S.H.Zhu, Phys.Lett. B451 (1999) 93• C.S.Li, J.M. Yang, B.Q. Hu, PRD48(1993)5425• C.S.Li, R.J.Oakes, J.M.Yang,Phys.Rev.D54(1996)6883• A. Czarnecki, K.Melnikov, Nucl.Phys.B544(1999)520• K.G.Chetyrkin,R.Harlander,T.Seidensticker,

Steinhauser, Phys.Rev.D60(1999)114015• A.Ghinculov, Y.P.Yao, Mod.Phys.Lett.A15(2000)925• M.Slusarczyk, hep-ph/0404249

Top decay

NLO QCD: -8.4%

M. Jezabek,J.H. Kuhn, Nucl.Phys.B314(1989)1

NNLO QCD: -2%,

M.Slusarczyk, hep-ph/0404249

Polarized Top Decay:

M.Fischer,S.Groote,J.G.Korner,M.C.Mauser,B.Lampe,Phys.Lett.B451(1999)406; M.Fischer,S.Groote,J.G.Korner,M.C.Mauser,Phys.Rev.D64(2001)017301;65(2002)054036; W.Bernreuther, M.Fuecker, Y. Umeda Phys.Lett. B582 (2004) 32

A. Brandenburg, Z.G. Si, P. Uwer, Phys.Lett. B539 (2002) 235.

Decay distributions: A. Brandenburg, M. Maniatis, Phys.Lett. B545

(2002) 139

FCNC top rare decay via SUSY QCD

C.S.Li, R.J.Oakes and J.M.Yang, PRD49(1994)293;56(1997) 3156(E)

J.M.Yang , C.S.Li, Phys.Rev.D49:3412-3416,1994, Erratum-ibid.D51:3974,1995

G.Couture, C.Hamzaoui and H.Konig, PRD52(1995)1713

G.Couture, M.Frank and H.Konig, PRD56(1997)4213

G.M.de Divitiis, R.Petronzio and L.Silvestrini, NPB504(1997)45

J.Guasch and J.Sola, NPB562(1999)3

J.J. Liu, C.S.Li, L.L.Yang, L.G.Jin., PLB 599 (2004) 99

Three mechanisms for Single top Production at NLO QCD at Hadron

Colliders

ud->W*->tb, M.C.Smith,S.Willenbrock,Phys.Rev.D54(1996)6696

C. S. Li, R.J. Oakes, J.M.Yang, H.Y. Zhou, PRD57 (1998) 2009

bu->td, G.Bordes,B.van.Eijk,Nucl.Phys.B435(1995)23;T.Stelzer, Z.SullivanS.Willenbrock,Phys.Rev.D56(1997)5919

bg->tW-, S.H. Zhu Phys. Lett. B 524 (2002) 283 ;537( 2002) 351(E)

Fully differential cross section, B. W. Harris, E. Laenen, L. Phaf, Z. Sullivan, S. Weinzierl, Phys.Rev. D66 (2002) 054024

Including the top quark decay Q.H. Cao, R.Schwienhorst, C.-P. Yuan Phys.Rev.

D71 (2005) 054023 Q.H. Cao, C.-P. Yuan Phys.Rev. D71 (2005) 054022 Q.H. Cao, R.Schwienhorst, J.A. Benitez, R.Brock , C.-P. Yuan hep-ph/0504230

J.Campbell, R. K. Ellis, F.Tramontano Phys.Rev. D70 (2004) 094012

Single Top FCNC productions ILC: C.S. Li, X.M. Zhang, S.H. Zhu, Phys. Rev D60 (1999)

077702 HERA: Belyaev, N.Kidonakis, Phys.Rev. D65 (2002) 037501 Hadron colliders: NLO QCD: N.Kidonakis, A.Belyaev, JHEP 0312 (2003) 004 SUSY-QCD: J.J.Liu, C.S.Li, L.L.Yang, L.G.Jin, NPB705(2005)3; MPLA19, 4

(2004) 317 NLO QCD ( Model-independent FCNC Couplings): J.J.Liu, C.S.Li, L.L.Yang, L.G.Jin, to be submitted to PRD

Single Top Production at e Collider

J.H.Kühn, C.Sturm, P.Uwer, Eur.Phys.J. C30 (2003) 169-182

In SM including QCD corrections (NLO, NNLO, resummation) at Tevatron and LHC

Total cross sections: P.Nason, S.Dawson and R.K.Ellis, Nucl.Phys. B303, (1988) 607 W.Beenakker, H.Kuijf, W.L.van Neerven and J.Smith, Phys.Rev. D40, (1989) 54 ;

pT and y spectra: P.Nason, S.Dawson and R.K.Ellis, Nucl.Phys. B327 (1989) 49W.Beenakker, W.L.van Neerven, R.Meng, G.A.Schuler and J.Smith, Nucl.Phys. B351 (1991) 507 ;

Double-differential spectra: M.L.Mangano, P.Nason and G.Ridolfi, Nucl.Phys. B373 (1992) 295 S.Frixione, M.L.Mangano, P.Nason and G.Ridolfi, Phys. Lett. B351 (1995)555

Resummation(LL): S.Catani, M.L.Mangano, P.Nason and L.Trentadue, Phys. Lett. B378 (1996)329;Nucl. Phys. B478 (1996)273 E.L.Berger and H.Contopanagos, Phys. Rev. D57 (1998)253

Resummation(NLL): N.Kidonakis and G.Sterman, Nucl. Phys. B505 (1997) 321 R.Bonciani, S.Catani, M.L.Mangano and P.Nason, Nucl. Phys. B529 424(1998)

Top Pair production

Recent development(include the soft-gluon corrections at NNLO):

N. Kidonakis, Int. J. Mod. Phys. A15 (2000)1245; Mod. Phys. Lett. A19(2004)405; hep-ph/0410116.N. Kidonakis, Phys. Rev. D64 (2001)014009; Int. J. Mod. Phys. A16 Suppl. 1A, 363 (2001);

N. Kidonakis, E. Laenen, S. Moch, and R. Vogt, Phys. Rev. D64 (2001)114001; Phys. Rev. D67 (2003)074037; Nucl. Phys. A715 (2003)549

N. Kidonakis and R. Vogt, Phys. Rev. D68 (2003) 114014; Eur. Phys. J. C33 (2004) s466.

Top Pair production

N. Kidonakis and R. Vogt Phys. Rev. D68 (2003) 114014

SUSY QCD at PHOTON-PHOTON COLLISION, H.Wang, C.S. Li, H.Y. Zhou, Y.P. Kuang Phys.Rev.D54:4374-4379,1996

SUSY QCD at Tevatron, C.S.Li, H.B. Hu, J.M Yang, C.G. Hu, Phys.Rev.D52:5014-

5017,1995, Erratum-ibid.D53:4112,1996 C.S. Li, H.Y. Zhou, Y. L. Zhu, J. M. Yang, PL B379

(1996) 135 SUSY QCD at LHC, H.Y.Zhou,C.S.Li, Phys.Rev.D55:4421-4429,1997 C.S. Li, C.P. Yuan, H.Y. Zhou PLB424 (1998) 76

(parity violation) NLO QCD effects in VV->tt at ILC, S. Godfrey & S.H. Zhu, hep-ph/0412261.

Top Pair productions

Spin Correlations in top pair production

e+e- colliders: H. X. Liu, C.S. Li, Z. J. Xiao Phys.Lett. B458 (1999) 393

A.Brandenburg, M. Maniatis Phys.Lett. B558 (2003) 79

Hadron colliders: W. Bernreuther, A. Brandenburg, Z.G. Si, P. Uwer Phys.Lett. B509 (2001) 53; Phys.Rev.Lett. 87 (2001) 242002; Int.J.Mod.Phys. A18 (2003) 1357

Polarized photon colliders: A. Brandenburg, Z.G. Si Phys.Lett. B615 (2005) 68

NLO QCD corrections to gg -> t tbar g, A.Brandenburg, S.Dittmaier, P.Uwer, S.Weinzierl, hep-ph/0408137

The interference between production and decay at Linear Colliders:

C. Macesanu Phys.Rev. D65 (2002) 07403 C.Macesanu, L.H. Orr Int.J.Mod.Phys. A16S1A (2001) 369; Phys.Rev.

D65 (2002) 014004

…

Other progress

(5) Factorization and re-summation

Factorization: separate perturbative and nonperturbative contributions to a process.

Re-summation: control the behavior of large logarithms.

Two techniques for factorization & re-summation :

(1) pQCD approach: analysis of Feynman diagrams (CSS)

(2) SCET (soft collinear effective theory) approach: effective Lagrangian and process-dependent operators (For details of SCET, see C. Bauer plenary talk)

The resummation formalism has been developed about two decades ago

• Y. Dokshitzer, D. Diakonov, S. I. Troian (DDT) (Phys.Lett.B79:269,1978; Phys.Rep.58:269,1980)

In order to implement momentum conservation, The resummation is performed in impact parameter b-space.

• G. Parisi, R. Petronzio (Nucl.Phys.B154:427,1979)• G. Curci, M. Greco, Y. Srivastava (Nucl.Phys.B159:451,1979)• J. Collins, D. E. Soper, G. Sterman (CSS) (Nucl.Phys.B250:199,1985)

Resummation in space is also possible

• G. Altarelli, R. K. Ellis, M. Greco, G. Martinelli (Nucl.Phys.B246:12,1984)

• R. K. Ellis, D. A. Ross, S. Veseli (Nucl.Phys.B503:309,1997)• R. K. Ellis, S. Veseli (Nucl.Phys.B511:649,1998)• Kulesza, Stirling (Nucl.Phys.B555:279,1999)

Tq

Tq

pQCD approach of resummation

Non-perturbative prescription

ansatz • J. Collins, D. E. Soper, G. Sterman (1985)• C. Davies, B. Webber, W. Stirling (Nucl.Phys.B256:413,1985)• G. A. Ladinsky, C. P. Yuan (Phys.Rev.D50:4239,1994)• F. Landry, R. Brock, P. M. Nadolsky, C. P. Yuan

(Phys.Rev.D67:073016,2003)

extrapolation • J. W. Qiu, X. F. Zhang (Phys.Rev.D63:114011,2001)

dispersive method• A. Guffanti, G. E. Smye (JHEP 0010:025,2000)

dependent factorization • X. D. Ji, J. P, Ma, F. Yuan (Phys.Rev.D71:034005,2005;

Phys.Lett.B597:299,2004)

*b

Tk

resummation in Higgs production

•I. Hinchliffe, S. F. Novaes (Phys.Rev.D38:3475,1988)

•R. P. Kauffman (Phys.Rev.D44:1415,1991; 45:1512,1992)

•C. P. Yuan (Phys.Lett.B283:395,1992)

•C. Balazs, C. P. Yuan (Phys.Lett.B478:192,2000)

•E. L. Berger, J. W. Qiu (Phys.Rev.Lett.91:222003,2003; Phys.Rev.D67:034026,2003)

•A. Kulesza, W. J. Stirling (JHEP 0312:056,2003)

•G. Bozzi, S. Catani, D. de Florian, M. Grazzini (Phys.Lett.B564:65,2003)

•B. Field (Phys.Rev.D70:054008,2004)

Current accuracy: next-to-next-leading logarithm (NNLL)

Tq

resummation in other processes

Gauge boson pair production•C. Balazs, C. P. Yuan (Phys.Rev.D57:6934-6947,1998)•C. Balazs, Ph.D thesis (hep-ph/9906422)

production•E. L. Berger, J. W. Qiu, Y. L. Wang (Phys.Rev.D71:034007,2005)

Single stop production•T. Plehn (Phys.Lett.B488:359-366,2000)

Polarized W and Z production at RHIC•A. Weber (Nucl.Phys.B403:545-571,1993)•P. Nadolsky, C. P. Yuan (Nucl.Phys.B666:31-55,2003)

Single slepton productionLL Yang, CS Li, JJ Liu, to be submitted to PRD

Tq

Recent developments

resummation with small-x effects•S. Berge, P. Nadolsky, F. Olness, C. P. Yuan (hep-ph/0410375,2004)

Global fit of the non-perturbative parameters•F. Landry, R. Brock, P. M. Nadolsky, C. P. Yuan (Phys.Rev.D67:073016,2003)•strong evidence for universality of the NP function

Universality of the resummed form factor•S. Catani, D. de Florian, M. Grazzini (Nucl.Phys.B596:299,2001)

Calculation of coefficient A3 (extracted from the three loop splitting functions)

•S. Moch, J. A. M. Vermaseren, A. Vogt (Nucl.Phys.B688:101,2004)•A. Vogt, S. Moch, J. A. M. Vermaseren (Nucl.Phys.B691:129,2004)

Tq

Threshold re-summation

Drell-Yan•G. Sterman (Nucl.Phys.B281:310,1987)•S. Catani, L. Trentadue (Nucl.Phys.B327:323,1989;353:183,1991)•A. Vogt (Phys.Lett.B497:228-234,2001)

Higgs•M. Kramer, E. Laenen, M. Spira (Nucl.Phys.B511:523,1998)•S. Catani, D. de Florian, M. Grazzini, P. Nason (JHEP 0307:028,2003)

Heavy quarks•S. Catani, M. L. Mangano, P. Nason, L. Trentadue

(Phys.Lett.B378:329,1996; Nucl.Phys.B478:273,1996)•R. Bonciani, S. Catani, M. L. Mangano, P. Nason (Nucl.Phys.B529:424,1998)

Current accuracy: NNLL for DY and Higgs, NLL for HQ

Joint re-summation

Drell-Yan•E. Laenen, G. Sterman, W. Vogelsang (Phys.Rev.D63:114018,2001)•A. Kulesza, G. Sterman, W. Vogelsang (Phys.Rev.D66:014011,2002)

Higgs•A. Kulesza, G. Sterman, W. Vogelsang (Phys.Rev.D69:014012,2004)

heavy quarks•A. Banfi, E. Laenen (Phys.Rev.D71:034003,2005)

SCET A natural frame for the proof of factorization

and the implement of re-summation • C. W. Bauer, S. Fleming, and M. Luke, Phys.Rev. D63 (2001) 014006• C.W.Bauer, S.Fleming, D.Pirjol, and I.W.Stewart, Phys.Rev. D63, 114020

(2001)• C.W.Bauer, D.Pirjol, and I.W.Stewart, Phys.Rev.Lett. 87, 201806 (2001)• C.W. Bauer, D.Pirjol, and I.W. Stewart, Phys.Rev.D 65, 054022 (2002) • M. Beneke, A.P. Chapovsky, M. Diehl, and Th. Feldmann, Nucl.Phys.B

643, 431 (2002)

Factorization and re-summation in B physics:• J. Chay, and C.Kim, Phys.Rev. D68 (2003) 071502; Phys.Rev. D68 (2003)

034013• S.W.Bosch, R.J.Hill, B.O.Lange, and M.Neubert, Phys.Rev.D 67, 094014

(2003)• C.W. Bauer, and A.V. Manohar, Phys.Rev.D 70, 034024 (2004) • M.Beneke, and Th.Feldmann, Nucl.Phys.B 685, 249 (2004)

Factorization and resummation in High energy hard process:

• Hard Scattering Factorization– C.W.Bauer, S.Fleming, D.Pirjol, I.Z.Rothstein, and I.W.Stewart,

Phys.Rev.D 66, 014017 (2002)

• Enhanced Nonperturbative Effects in Z Decays to jets– C.W.Bauer, A.V.Manohar and M.B.Wise, Phys.Rev.Lett.91, 122001

(2003)– C.W.Bauer, C.Lee, A.V.Manohar and M.B.Wise, Phys.Rev.D 70,

034014 (2004)

• Threshold re-summation– DIS process: A.V.Manohar, Phys.Rev.D 68, 114019 (2003)– Drell-Yan process: A.Idilbi and X.D.Ji, hep-ph/0501006

• QT and joint re-summation– Y.Gao, C.S.Li, and J.J.Liu, hep-ph/0501229

Outline of SCET

Steps = matching + running QCD to SCETI: integrate out modes of

, left with collinear and usoft modes

Decouple transformations in SCETI

SCETI to SCETII : integrate out collinear modes of

)( 2 Q

222 Qp

422 Qp

Application to QT re-summation in Higgs production

A re-derivation of NNLL DDT formula (Y.Gao, C.S.Li, and J.J.Liu, hep-ph/0501229)

)Q,](xC)[fQ,](xC[f)Q,x,(xW

)](Blog)(A[Q),(QS

)Q,x,(xWe1

T2gbb/pT1gaa/pT21gg

2

2

2

2

Tg

,T21gg

Q),(QS

222)0(

21

2

2

Tg

ss

Q

Q

baTT

resum

Qd

dQ

d

dydQdQ

d

T

Numerical evaluation and non-perturbative prescription are simpler in QT space (R. K. Ellis, S.

Veseli, Nucl.Phys.B511:649,1998)

Provided that initial and final states in any process are confined to be soft or collinear, SCET can be applied

The multiple scales problems and nonperturbative effects can be taken into account systematically

(6) Summary(6) Summary

1. QCD effects are significant in almost every case.2. QCD effects (in Higgs physics, in SUSY, in top

physics etc.) are essential in testing SM and searching new physics beyond the SM.

3. Evaluating of QCD effects is complicated at NNLO. So far we don’t know how to calculate NNLO in general case.

4. Re-summation techniques are important in determining observables of high energy hard processes. Current accuracy is up to NNLL.

5. SCET simplifies the proof of factorization and re-summation at leading order of λ(C. Bauer etal.), and the case of next order is worthy of investigating in the future.

6. Need more work!

Thanks for your attention!