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SANC: precision calculations for the SM

processes

D. Bardin & L. Kalinovskaya on behalf of SANC group

Laboratory of Nuclear Physics, Joint Institute for Nuclear Research, Dubna,

Russia

April 23, 2007

D. Bardin & L. Kalinovskaya on behalf of SANC group SANC: precision calculations... ACAT 2007, Amsterdam

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SAN

SANC: Support of Analytic andNumerical Calculations for Colliders

SANC v1.10 is accessible from two servers:at Dubna http://sanc.jinr.ru/ (159.93.75.10)and CERN http://pcphsanc.cern.ch/ (137.138.100.80)


SANC GROUP

D. Bardin, L. Kalinovskaya,A. Arbuzov∗, S. Bondarenko∗, P. Christova,G. Nanava∗∗, W. von Schlippe∗∗∗

PhD students: A. Andonov, V. Kolesnikov, L. Rumyantsev,R. Sadykov, E. UglovStudent: O. Karamyshev

In cooperation with JINR ATLAS muon group:G. Chelkov, I. Boyko, M. Demichev, A. Scherbakov

Dzhelepov Laboratory of Nuclear Problems, JINR, Dubna∗Bogoliubov Laboratory of Theoretical Physics, JINR, Dubna∗∗Presently at IFJ–PAN, Krakow, Poland∗∗∗PNPI, Gatchina, St. Petersburg∗∗∗∗Bishop Konstantin Preslavsky University, Shoumen, Bulgaria

Supported by INTAS 03-51-4007 and by RFBR (project N 07-02-00932-)


Outline

◮ Tools for theoretical support of HEP experiments


Outline


◮ Present status SANC v.1.10


Outline



◮ Basic notion: precomputation, structures, form

factors (FF), helicity amplitudes (HA),accompanying (glue/brem)sstrahlung (BR)


Outline





◮ SANC Output


Outline





◮ SANC Output

◮ Some physical results for processes with• 3 legs

• 4 legs• 5 legs


Tools for theoretical support of HEP experiments

Selection principle: whom we compared with...

◮ Universal tools — MC generators, precision ∼ 10%




◮ Universal tools — MC generators, precision ∼ 10%◮ GRACE-tree — the system, any process up to 1, 2 → 4, tree level

◮ CompHEP — the system, any process up to 2 → 6, tree level

◮ PYTHIA — the code, rich collection of processes







◮ Dedicated precision generators — ≤ .1%:◮ HORACE — the code, one-loop improved

◮ WGRAD2, ZGRAD2 — the code, one-loop improved







◮ Dedicated precision generators — ≤ .1%:◮ HORACE — the code, one-loop improved

◮ WGRAD2, ZGRAD2 — the code, one-loop improved

◮ Precision tools — theoretical precision ≤ .1%:◮ FeynArts — automatic system up to 2 → 3 processes

◮ GRACE-loop — any process up to 2 → 2, several 2 → 3

◮ SANC — the IDE, aimed at any process up to 2 → 3;

Ref.: SANCscope — v.1.00 Comput. Phys. Comm. 174 (2006) 481


Present status version 1.10, processes available

LK → Root

SANC

QED

EWPrecomputation

Processes

3 legs

3 b

H −> A A

H −> A Z

H −> Z Z

H −> W W

Z −> W W

b2 f

H −> f f

Z −> nu nu

Z −> f f

W −> f f’

t −> W b

t −> W b (FF)

t −> W b (HA)

t −> W b (BR)

4 legs

QCD

Root

SANC

QED

EW

Precomputation

Processes

3 legs

4 legs

4 f

Neutral Current

Bhabha

f1 f1 −> f f

Charged Current

f1 f1’ −> f f’

t −> b l nu

2 f2b

Neutral Current

f f −> A A

A A −> f f

f1 f1 −> H A

H −> f1 f1 A

f1 A −> f1 H

f f −> Z A

f1 f1 −> Z Z

f1 f1 −> H Z

H −> f1 f1 Z

Charged Current

QCD

Notation for folders:b – any boson; f (f1) – any fermion (massless) fermion; A – a photon;for files: the same but t, b mean top and bottom quarks.

For many processes in SANC there are MC event generators.


Precomputation, amplitudes, form factors ...

◮ Precomputation: to precompute as manyone-loop diagrams and derived quantities

(renormalization constants, etc) as possible





◮ Covariant Amplitudes (CA) and scalar Form

Factors (FF) — Fi

A ∝ γµF1 + σµνqνF2






Factors (FF) — Fi


◮ Helicity Amplitudes (HA) — H{λi}(Fi)

standard approach: O ∝ |A|2while in terms of HAs: O ∝

∑

{λi} |H{λi}|2






Factors (FF) — Fi




∑

{λi} |H{λi}|2◮ Accompanying Bremsstrahlung (BR)






Factors (FF) — Fi




∑


◮ Analytic calculations with FORM3.0



◮ Precomputation: to precompute as many

one-loop diagrams and derived quantities(renormalization constants, etc) as possible

◮ Covariant Amplitudes (CA) and scalar FormFactors (FF) — Fi




∑


◮ Analytic calculations with FORM3.0 LK →


From analytic results to numbers

◮ Virtual corrections

dΓ(dσ) ∼∑

λiλjλkλl

∣

∣

∣H(

FBorn+1loop+2loop)

λiλjλkλl

∣

∣

∣

2




dΓ(dσ) ∼∑

λiλjλkλl

∣

∣

∣H(

FBorn+1loop+2loop)

λiλjλkλl

∣

∣

∣

2

◮ Real corrections




dΓ(dσ) ∼∑

λiλjλkλl

∣

∣

∣H(

FBorn+1loop+2loop)

λiλjλkλl

∣

∣

∣

2


◮ Soft bremsstrahlung

◮ Hard bremsstrahlung

either from semi-analytic or MC calculations




dΓ(dσ) ∼∑

λiλjλkλl

∣

∣

∣H(

FBorn+1loop+2loop)

λiλjλkλl

∣

∣

∣

2


◮ Soft bremsstrahlung

◮ Hard bremsstrahlung

either from semi-analytic or MC calculations

◮ s2n package to generate FORTRAN codesSANC includes its own FORTRAN library for numerical calculation ofPassarino–Veltman functions and use LoopTools as an alternative

T. Hahn and M. Perez-Victoria; http://www.feynarts.de/looptools/


Types of SANC Outputs:

◮ FORTRAN modules

for use in MC generators by ourselves or by the others;

◮ Standalone MC generators :

a) generator for H → 4µ decay in the single Z poleapproximation;

b) generators for NC and CC Drell–Yan processes;c) generator for t → blν decay;

◮ Contribution to tuned comparison, an impact on

competition of precision MC generators at the LHC:Les Houches Workshop Proceedings, 2006 and

Tevatron for LHC Report, 2007.


SANC application for processes

(F) & (H)→ s2n → MC



(F) & (H)→ s2n → MC

◮ 1 → 2 decays LK !



(F) & (H)→ s2n → MC


◮ t → blν decay



(F) & (H)→ s2n → MC



◮ f1f1HA → 0: three cross channels



(F) & (H)→ s2n → MC




◮ f1f1HZ → 0: two cross channels



(F) & (H)→ s2n → MC





◮ Drell–Yan-like W and Z production



(F) & (H)→ s2n → MC





◮ Drell–Yan-like W and Z production

◮ H → 4µ decay



1 → 2 decay

LK →◮ Old stuff, build-in MC generators are implemented



1 → 2 decay


◮ Benchmark case 1:

Benchmark Results for Γ(Z → bb) decay

ΓBorn ΓBorn+virt+soft ΓTotal

Semi-Analytic 0.355428 0.335345 0.358738MC , 100 k 0.358742 ± 0.000718



1 → 2 decay


◮ Benchmark case 1:

Benchmark Results for Γ(Z → bb) decay

ΓBorn ΓBorn+virt+soft ΓTotal

Semi-Analytic 0.355428 0.335345 0.358738MC , 100 k 0.358742 ± 0.000718

◮ Refs.A. Andonov, S. Jadach, G. Nanava, Z. Was,Acta Phys. Polon. B34 (2003) 2665 hep-ph/0212209;

G. Nanava, Z. Was, Acta Phys. Pol. B34 (2003) 4561;

hep-ph/0303260 LK →



t → blν decay

Implemented/done: LK !



t → blν decay


◮ total width and various distributions;



t → blν decay



◮ with one-loop EW and QCD corrections;



t → blν decay




◮ complete calculations and the pole approximation;



t → blν decay





◮ MC integrators and event generator;



t → blν decay






◮ comparison with world literature.



t → blν decay






◮ comparison with world literature.

◮ Ref.SANCnews: Sector 4f , Charged CurrentA. Arbuzov, D. Bardin, S. Bondarenko, P. Christova,L. Kalinovskaya, G. Nanava, R. Sadykov, W. vonSchlippe.Submitted to EPJC, hep-ph/0703043,



3 channels of f1f1HA → 0

LK !◮ The common CA for all four momenta incoming:

p1

p2 p3

p4

f

f γ

H

The f fγH → 0 process.





p1

p2 p3

p4

f

f γ

H


◮ The particular channels:

p1

p2 p3

p4

f

f γ

H

The annihilation channel

H

γ

f

fp2

p1

p3

p4

The decay channel

γ

f f

H

p1 p4

p3p2

The eγ → eH channel





p1

p2 p3

p4

f

f γ

H


◮ The particular channels:

p1

p2 p3

p4

f

f γ

H

The annihilation channel

H

γ

f

fp2

p1

p3

p4

The decay channel

γ

f f

H

p1 p4

p3p2

The eγ → eH channel

◮ Ref.The three channels of the process f1f1HA → 0 in the SANC framework,D. Bardin, S. Bondarenko, L. Kalinovskaya, G. Nanavaand L. Rumyantsev. Submitted to EPJC, hep-ph/0702115.


Annihilation channel f1f1 → HA

100 150 200 250 300 350 400M

H, GeV

10-3

10-2

10-1

σ, fb

s=500 GeV s=1500 GeV√

√

One-loop corrected cross section of the Higgs boson production viaannihilation process, as a function of the Higgs boson mass, MH .

Good “visual” agreement with: A. Djouadi, V. Driesen, W. Hollik

and J. Rosiek, Nucl. Phys. B 491 (1997) 68


Decay channel H → µ+µ−γ

0 50 100 150Mµµ

, GeV10

-14

10-13

10-12

10-11

10-10

10-9

10-8

10-7

10-6

dΓ/d

Mµµ

, GeV

Born levelOne-loop level

The Mµ+µ− invariant mass distribution, Born and one-loop levels,

MH =150GeV.


The production channel eγ → eH:

SANC and Ref. E. Gabrielli et al. [⋆].

MH/√

s 500 1000 1500

SANC ⋆ δ SANC ⋆ δ SANC ⋆ δ

80 8.40 8.38 -0.2 9.31 9.29 -0.2 9.76 9.74 -0.2100 8.85 8.85 0 9.95 9.94 -0.1 10.48 10.5 -0.2120 9.77 9.80 0.3 11.16 11.2 0.4 11.80 11.8 0140 11.76 11.8 0.3 13.68 13.7 0.1 14.52 14.6 0.6160 20.91 21.1 0.9 24.82 25.0 0.7 26.48 26.6 0.5180 20.67 20.9 1.1 25.04 25.3 1.0 26.81 27.0 0.7200 16.99 17.2 1.2 21.05 21.2 0.7 22.64 22.8 0.7300 5.90 5.97 1.2 8.44 8.53 1.0 9.33 9.43 1.1400 1.64 1.64 0 2.74 2.78 1.5 3.15 3.18 1.0

H production channel: cross sections σ (fb) and relative differenceδ (%) between two calculations: SANC andRef. E. Gabrielli, V. A. Ilyin and B. Mele, Phys. Rev. D 56 (1997)5945; [Erratum-ibid. D 58 (1998) 119902].



2 channels of f1f1HZ → 0: CA

LK !◮ f1(p1)f1(p2)Z (p3)H(p4) → 0: 6 structures, 6 form factors

AffHZ = k{[

v (p1)(

γνγ+σf F+

0 (s, t) − /p3γ+(p1)νF+

1 (s, t)

−/p3γ+(p2)νF+

2(s, t)

)

u (p2) εZ

ν(p3)

]

+[

σf → δf , γ+ → γ− F+

i (s, t) → F−

i (s, t)]}

γ± = 1 ± γ5 , σf = vf + af , δf = vf − af

k = − ig 2

4c2W

MZ

M2Z− s



2 channels of f1f1HZ → 0: CA

LK !◮ f1(p1)f1(p2)Z (p3)H(p4) → 0: 6 structures, 6 form factors

AffHZ = k{[

v (p1)(

γνγ+σf F+

0 (s, t) − /p3γ+(p1)νF+

1 (s, t)

−/p3γ+(p2)νF+

2(s, t)

)

u (p2) εZ

ν(p3)

]

+[

σf → δf , γ+ → γ− F+

i (s, t) → F−

i (s, t)]}

γ± = 1 ± γ5 , σf = vf + af , δf = vf − af

k = − ig 2

4c2W

MZ

M2Z− s

◮ Ref.: SANCnews: Sector ffbbD. Bardin, S. Bondarenko, L. Kalinovskaya, G. Nanava,L. Rumyantsev,

and W. von Schlippe; submitted to Comput. Phys. Commun.;

hep-ph/0506120


Annihilation channel e+e− → HZ :

Grace-Loop & Denner et al. & SANC

√s, GeV MH , GeV Grace-Loop[1] [2] SANC

500 100 4.1524 4.1524 4.1524500 300 6.9017 6.9017 6.90171000 100 −2.1656 −2.1656 −2.16561000 300 −2.4995 −2.4995 −2.49951000 800 26.1094 26.1094 26.10942000 100 −11.5413 −11.5414 −11.54142000 300 −12.8226 −12.8226 −12.82262000 800 11.2468 11.2468 11.2468

Corrections to the total cross section in percent in α scheme.[1] G. Belanger et al., Preprint hep-ph/0308080.[2] A. Denner, J. Kublbeck, R. Mertig and M. Bohm, Z.Phys. C56 (1992) 261.


Decay channel H → Zf1f1(γ):

distributions over m2µ+µ−(γ)

2, GeV2)γ-(µ+µs = m

200 400 600 800 1000 1200 1400

-1 G

eV-9

, 10

dsΓd

0

1

2

3

4

5

6

7

) Invariant mass)^2γ- (µ+ µ/ds (s), where s is (Γ d

BORN Born+1loop, α scheme


H → Zf1f1: the origin of the Coulomb peak

H → Zγ width does not vanish for an on-shell photon with Q2γ

= 0:

H

Z

γ

H

Z

f1

f1

γ

Therefore, the one-loop amplitude for H → Zf1 f1 with virtualphoton exchange will show a ∼ 1/s behavior (with s = −Q2

γ).

This, in turn, will lead to the ∼ 1/s behavior of both the doubleand single differential widths.

The 1/s region is very narrow and is largely washed out not only by

a soft cut on the variable s but even by the plain s-integration.


H → Zf1f1: benchmark case 3

LK→ The double differential widths for H → e+e−Z decay in α-scheme.First row: the double differential decay width d2Γ/ds d cos ϑl · 108GeV−1

at the Born level; second row: the double differential decay width atthe 1-loop level; third row: relative correction δ = d2Γ1−loop/d2ΓBorn.Numerical values are truncated to 6 figures.

H → e+e−Z

Part 1, d2Γ/ds d cosϑl · 108, GeV−1

√s, GeV 1 3 10 28

Born 0.02019 0.02144 0.03505 0.042611-loop cosϑl = ±0.9 0.21060 0.04321 0.03874 0.04602

δ 9.43022 1.01508 0.10537 0.07984Born 0.07914 0.07964 0.08478 0.043531-loop cosϑl = ±0.5 0.21495 0.09898 0.09150 0.04701

δ 1.71589 0.24281 0.07922 0.07976Born 0.10546 0.10562 0.10698 0.043941-loop cosϑl = 0.0 0.21695 0.12394 0.11510 0.04745

δ 1.05716 0.17343 0.07586 0.07972 LK→D. Bardin & L. Kalinovskaya on behalf of SANC group SANC: precision calculations... ACAT 2007, Amsterdam


CC Drell–Yan: benchmark case 2, partonic level

LK→CMS differential cross sections in pb for ud → e+νe√

s GeVcos θ 40 80 120

-0.9 Born 3.33973 9361.58 11.3047Born + one-loop 3.50144 9379.90 22.2332

-0.5 Born 2.08155 5834.78 7.04592Born + one-loop 2.17360 5845.82 10.8827

0.0 Born 0.92513 2593.23 3.13152Born + one-loop 0.96582 2600.17 4.43144



LK→


CC and NC Drell–Yan processes distributions

CC:(

qq′

g(γ)q

)



CC:(

qq′

g(γ)q

)

⊗(

pT

MT

)

MT =√

2pℓTpν

T (1 − cosϕℓν)



CC:(

qq′

g(γ)q

)

⊗(

pT

MT

)

⊗(

µe

)

µ — bare

e — γ recombination



CC:(

qq′

g(γ)q

)

⊗(

pT

MT

)

⊗(

µ

e

)

NC:(

qq

g(γ)q

)

⊗(

pT

Mℓ+ℓ−

)

⊗(

µe

)



CC:(

qq′

g(γ)q

)

⊗(

pT

MT

)

⊗(

µe

)

NC:(

qq

g(γ)q

)

⊗(

pT

Mℓ+ℓ−

)

⊗(

µ

e

)

done but not yet implemented.


δ definition

The distributions are produced for the cross-section

σ and the relative corrections δ,where the last is defined by

δ = σ1−loop/σBorn − 1 for NLO QCD and EWcorrections originating from the qq′ sub-processand by

δ = σg(γ)q/σBorn for corrections originating fromthe gluon (photon) induced process.


CC DY: σ, MT distribution

[GeV]TM50 55 60 65 70 75 80 85 90 95 100

[pb/

GeV

]T

/dM

σd

0

20

40

60

80

100

120 LONLO muonsNLO electrons


CC DY: δ, MT distribution

[GeV]TM50 55 60 65 70 75 80 85 90 95 100

[%]

δ

-8

-7

-6

-5

-4

-3

-2

-1

0 bare muons

recomb.γ


CC DY: δ, PℓT distribution

[GeV]TP25 30 35 40 45 50

[%]

δ

-10

-8

-6

-4

-2

0

bare muons qγbare muons+

recomb.γ qγ recomb+γ


CC DY: δ, MT distribution

[GeV]TM50 55 60 65 70 75 80 85 90 95 100

[%]

δ

-8

-7

-6

-5

-4

-3

-2

-1

0

bare muons qγbare muons+

recomb.γ qγ recomb+γ


NC DY: σ, Mℓ+ℓ− distribution

[GeV]-l+lM50 55 60 65 70 75 80 85 90 95 100

[pb/

GeV

]- l+ l

/dM

σd

0

10

20

30

40

50 LONLO muons


NC DY: δ, Mℓ+ℓ− distribution

[GeV]-l+lM50 55 60 65 70 75 80 85 90 95 100

[%]

δ

-20

0

20

40

60

80

bare muons


QCD-EW INTERPLAY. CC DY: δ, MT distribution

QCD EW

[GeV]TM50 55 60 65 70 75 80 85 90 95 100

[%

]δ

-100

-80

-60

-40

-20

0

bare muons

[GeV]TM50 55 60 65 70 75 80 85 90 95 100

[%

]δ

-8

-7

-6

-5

-4

-3

-2

-1

0 bare muons

recomb.γ


QCD-EW INTERPLAY. NC DY: δ, Mℓ+ℓ− distribution

QCD EW

[GeV]-l+lM50 55 60 65 70 75 80 85 90 95 100

[%

]δ

-100

-80

-60

-40

-20

0

bare muons

[GeV]-l+lM50 55 60 65 70 75 80 85 90 95 100

[%

]δ

-20

0

20

40

60

80

bare muons


Drell–Yan processes: tuned comparison

TEV4LHC WorkshopList of participants:

◮ HORACE — C.C. Calame, G. Montagna, O. Nicrosini, A. Vicini(PAVIA)

◮ SANC — SANC group (JINR)

◮ W(Z)GRAD2 — U. Baur, D. Wackeroth (FNAL)


A tuned triple comparison within TEV4LHC workshop

(FERMILAB–CONF–07–052)

WGRADSANCHORACEbare utspp!W+ ! e+�eLHC

MT (e+�e) [GeV℄

� [%℄

10095908580757065605550

86420�2�4�6�8�10�12

WGRADSANCHORACEbare utspp! W+ ! �+��LHC

MT (�+��) [GeV℄

� [%℄

10095908580757065605550

76543210�1�2�3The relative correction ∆ due to electroweak O(α) corrections to theMT distribution for single W + production with bare cuts at the LHC.



H → Zf1f1: a MC generator for H → 4µ decay

Taking into account:— identity of muons;— one photon radiation;— one-loop EW virtual corrections in the resonance approximation:

f

f

HZ

one − loop

f

f

(approximation is valid for 130 ≤ MH ≤ 160 GeV), event generatorwas created and transferred for use to JINR ATLAS muon group.


MC H → 4µ: Prophecy4f

Precise predictions for the Higgs-boson decayH → W W / Z Z → 4 leptons.

A. Bredenstein, A. Denner, S. Dittmaier,M.M. Weber, MPP-2005-24, PSI-PR-06-05,

Apr 2006. e-Print Archive: hep-ph/0604011

Les Houches Physics at TeV Colliders 2005,

Standard Model and Higgs working group:Summary report.

C. Buttar et al. Apr 2006.e-Print Archive: hep-ph/0604120


MC H → 4µ: Prophecy4f & SANC

Partial with in 10−7 GeV

MH , GeV 120 130 140 150 160

Prophecy4f 0.7053(3) 2.3769(9) 6.692(2) 16.807(6) 40.06(1)

SANC (Gµ) 0.7197(3) 2.4079(8) 6.743(2) 16.842(5) 39.62(2)

δ,% 2.04 1.01 0.76 0.21 -1.10

SANC (α) 0.6938(2) 2.343(1) 6.594(2) 16.534(5) 39.15(1)

Comparison for partial width for decay H → 4µ in Gµ scheme forMH = 140 GeV between Prophecy4f and SANC.


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