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Bogolyubov Readings - 2010, Dubna 1 HEAVY QUARK JET PRODUCTION AT TEVATRON IN THE REGGE LIMIT OF QCD V.A. Saleev Samara State University, Samara, Russia and Samara Aerospace State University, Samara, Russia In collaboration with B. A. Kniehl

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HEAVY QUARK JET PRODUCTION AT TEVATRON IN THE REGGE LIMIT OF QCD

V.A. Saleev Samara State University, Samara, Russia and Samara Aerospace State University, Samara, Russia In collaboration with B. A. Kniehl and A. V. Shipilova

V.A. Saleev,Heavy quark jet production at Tevatron in the Regge limit of QCD

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Outlook

  • 1. Introduction
  • 2. Particle production in the Regge kinematics
  • 3. Effective vertices in the MRK and QMRK, and high-energy factorization
  • 4. Inclusive jet and prompt photon production at Tevatron
  • 5. Inclusive b and b + ¯

b production at Tevatron

  • 6. Associated b + γ, c + γ production at Tevatron
  • 7. Conclusions

V.A. Saleev,Heavy quark jet production at Tevatron in the Regge limit of QCD

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Particle production in the Regge kinematics

−PB PA P ′

B

P ′

A

PC

1 t2 1 t1

SAB = (PA + PB)2, SA′C = (PA′ + PC)2, SB′C = (PB′ + PC)2 SA′C, SB′C, P 2

C , P 2 T C ≪ SAB,

(PA · PA′) ≪ (PA · PC) ≪ (PA · PB′) yA′ ≫ yC ≫ yB′

V.A. Saleev,Heavy quark jet production at Tevatron in the Regge limit of QCD

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Electron Reggeization in QED:

  • M. Gell-Mann, M. L. Goldberger, F. E. Low, E. Marx, and F. Zachariasen, 1964.

Quark Reggeization in QCD:

  • V. S. Fadin and V. E. Sherman, 1976

Qluon Reggeization in QCD:

  • E. A. Kuraev, L. N. Lipatov, and V. S. Fadin, 1975
  • I. I. Balitsky and L. N. Lipatov, 1978

V.A. Saleev,Heavy quark jet production at Tevatron in the Regge limit of QCD

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b¯ b−jet production in the multi-Regge kinematics

R Q R y2 y¯

b

yb y1 y1 ≫ yb ≫ y¯

b ≫ y2

AMRK ∼ ΓR

P P ×

s1 t1 ωR(t1) × Γb

RQ ×

s t ωQ(t) × Γ

¯ b QR ×

s2 t2 ωR(t2) × ΓR

P P

V.A. Saleev,Heavy quark jet production at Tevatron in the Regge limit of QCD

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b¯ b−jet production in the quasi-multi-Regge kinematics

R R y2 y¯

b

yb y1 y1 ≫ yb ≃ y¯

b ≫ y2

AQMRK ∼ ΓR

P P ×

s1 t1 ωR(t1) × Γb¯

b RR ×

s2 t2 ωR(t2) × ΓR

P P

σ(PP → b¯ bX) = ΦR ⊗ ˆ σ(RR → b¯ b) ⊗ ΦR

V.A. Saleev,Heavy quark jet production at Tevatron in the Regge limit of QCD

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b−jet production in the multi-Regge kinematics

Q R y2 ≃ y¯

b

yb y1 y1 ≫ yb ≫ y¯

b ≃ y2

R Q y2 y¯

b

y1 ≃ yb y1 ≃ yb ≫ y¯

b ≫ y2

AQMRK ∼ ΓQ

P P ×

s1 t1 ωR(t1) × Γb

QR ×

s2 t2 ωQ(t2) × ΓR

P P

σ(PP → bX) = ΦQ ⊗ ˆ σ(QbR → b) ⊗ ΦR

V.A. Saleev,Heavy quark jet production at Tevatron in the Regge limit of QCD

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P1 = E1(1, 0, 0, 1), P2 = E2(1, 0, 0, −1), S = 4E1E2 (n+)µ = P µ

2 /E2,

(n−)µ = P µ

1 /E1,

k± = k · n± = kµn±

µ

q1 = x1P1 + q1T , q2 = x2P2 + q2T , t1 = −q2

1 = −q2 1T ,

t2 = −q2

2 = −q2 2T

V.A. Saleev,Heavy quark jet production at Tevatron in the Regge limit of QCD

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Vertex functions: g(k) + Q(q) → q(k + q) : γ±

µ (q, k) = γµ + ˆ

q n± k± , Q(q1) + ¯ Q(q2) → g(q1 + q2) : γ+−

µ

(q1, q2) = γµ − ˆ q1n−

µ

q−

2

− ˆ q2n+

µ

q+

1

V.A. Saleev,Heavy quark jet production at Tevatron in the Regge limit of QCD

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Effective vertices in the QMRK approach The QMRK approach is based on effective quantum field theory implemented with the non-Abelian gauge-invariant action: Reggeized gluons (R),

  • L. N. Lipatov, 1995,

Reggeized quarks (Q), L. N. Lipatov and M. I. Vyazovsky, 2001 Feynman rules for the effective theory:

  • E. N. Antonov, L. N. Lipatov, E. A. Kuraev, and I. O. Cherednikov, 2005
  • L. N. Lipatov and M. I. Vyazovsky, 2001

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RR → g Cg,µ

RR(q1, q2) = −gsf abc q+ 1 q− 2

2√t1t2

  • (q1 − q2)µ + (n+)µ

q+

1

  • q2

2 + q+ 1 q− 2

  • − (n−)µ

q−

2

  • q2

1 + q+ 1 q− 2

  • Q ¯

Q → γ Cγ,µ

Q ¯ Q(q1, q2) = −ieeq

  • γµ − ˆ

q1 (n−)µ q−

1 + q− 2

− ˆ q2 (n+)µ q+

1 + q+ 2

  • RQ → q

CRQ→q(q1, q2) = −igsT aγ(−)

µ

(q1, q2)Π(+)µ

T

(q2) Π(+)µ

T

(q2) = qµ

2T

| q2T |, Π(+)µ

T

(q2) = −x2E2(n+)µ | q2T | .

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RQ → γq CRQ→γq

µ

(q1, q2, k1, k2) = −eeqgsT bΠ(+)ν

T

(q2)

  • γν

ˆ q1 − ˆ k2 (q1 − k2)2 γ(−)

µ

(−k2, q1)+ γµ ˆ k1 + ˆ k2 (k1 + k2)2 γ(−)

ν

(q2, q1) − ˆ q1 n−

µ n− ν

q−

2 k− 2

  • V.A. Saleev,Heavy quark jet production at Tevatron in the Regge limit of QCD
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|M(RR → g)|2 = 3 2παs k2

T .

|M(QbR → b)|2 = 2 3παs k2

T .

|M(Q ¯ Q → γ)|2 = 4 3παeq( q2

1T +

q2

2T ).

We have k2

T =

q2

1T +

q2

2T + 2|

q1T || q2T | cos φ12, where q1T and q2T are the transverse momenta of the Reggeized quark and gluon, respectively, and φ12 is the azimuthal angle enclosed between them.

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|M(R + R → b + ¯ b)|2 = 256π2α2

s

1 2Nc MA + Nc 2(N 2

c − 1)MNA

  • ,

where MA = t1t2 ˜ t˜ u −

  • 1 + α1β2S

˜ u + α2β1S ˜ t 2 , MNA = 2 S2 α1β2S2 ˜ u + S 2 + ∆ ˆ s α2β1S2 ˜ t + S 2 − ∆ ˆ s

  • − t1t2

x1x2ˆ s 1 ˜ t − 1 ˜ u

  • (α1β2 − α2β1) + x1x2ˆ

s ˜ t˜ u − 2 S

  • ,

∆ = S 2

  • ˜

u − ˜ t + 2S(α1β2 − α2β1) + t1 β1 − β2 β1 + β2 − t2 α1 − α2 α1 + α2

  • ,

˜ t = ˆ t − m2, ˜ u = ˆ u − m2, t1 = −q2

1, t2 = −q2 2, α1 = 2(k1 · P2)/S, α2 = 2(k2 · P2)/S,

β1 = 2(k1 · P1)/S, and β2 = 2(k2 · P1)/S. Here, the Mandelstam variables are defined as ˆ s = (q1 + q2)2, ˆ t = (q1 − k1)2, ˆ u = (q2 − k1)2, S = (P1 + P2)2.

V.A. Saleev,Heavy quark jet production at Tevatron in the Regge limit of QCD

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|M(QR → qγ)|2 = −16 3 π2ααse2

q

x1S b2ˆ sˆ ut2

  • w0 + w1S + w2S2

, w0 = b2

1t2(t1 − ˆ

u) − b1b2(t2ˆ t + 2t2ˆ u + ˆ tˆ u) − b2

2

  • t1t2 + t2(ˆ

t + ˆ u) + t1ˆ u + ˆ uˆ t

  • ,

w1 = −b2x2

  • 2a1b2(t1 + ˆ

t) + a1b1(t2 + ˆ t) + a2b1(t2 + ˆ u)

  • ,

w2 = a1b2x2

2

  • a1b2
  • 1 + ˆ

s ˆ u

  • − a2b1
  • ,

V.A. Saleev,Heavy quark jet production at Tevatron in the Regge limit of QCD

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|M(Q ¯ Q → gγ)|2 = −128 9S π2ααse2

q

x1x2 a1a2b1b2ˆ tˆ u

  • w0 + w1S + w2S2 + w3S3

, w0 = −t1t2(t1 + t2) + ˆ tˆ u(ˆ t + ˆ u), w1 = x2t1(a1ˆ t + a2ˆ u) + x1t2(b2ˆ t + b1ˆ u) + t1t2(a1 − a2)(b1 − b2) + ˆ tˆ u(2a1b2 + x1b1 + x2a2) w2 = x2

2a1a2t1 + x2 1b1b2t2 + a1b2ˆ

t(x2a1 + a2b2) + a2b1ˆ u(x1b1 + a2b2), w3 = a1a2b1b2 a1b2ˆ t ˆ u + a2b1ˆ u ˆ t

  • .

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|M(Qr ¯ Qr → qf ¯ qf)|2 = − 64π2α2

s

9x1x2ˆ s2

  • w0 + w1S + w2S2

, w0 = x1x2ˆ s ˜ t + ˜ u

  • ,

w1 = −2x2

2α1α2t2 − 2x2 1β1β2t1 + x1x2{(α1β2 + α2β1)(ˆ

s + t1 + t2) + x1x2(ˆ s − 2m2) + + x1[β1(t1 + ˜ u) + β2(t1 + ˜ t)] + x2[α1(t2 + ˜ t) + α2(t2 + ˜ u)]}, w2 = −2x1x2(α1β2 − α2β1)2.

V.A. Saleev,Heavy quark jet production at Tevatron in the Regge limit of QCD

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|M(Qr ¯ Qr → qr¯ qr)|2 = 64π2α2

s

27x1x2a2b1ˆ s2ˆ t2 (w0 + w1S + w2S2) w0 = x1x2ˆ sˆ t

  • t1ˆ

t(3a2b1 − x1b2) + t2ˆ t(3a2b1 − x2a1) + t1t2(x2a2 − x1b2) − x1x2ˆ t2 + + ˆ sˆ t

  • 6(a1b1 + a2b2) + 5(2a2b1 + a1b2)
  • w1

= ˆ t

  • t1x1a2b2
  • 6b1ˆ

t(a2b1 − a1b2) − x2ˆ s(x1b1 + a2b1 − a1b2)

  • +

+ t2x2a1b1

  • 6a2ˆ

t(a2b1 − a1b2) − x1ˆ s(x2a2 + a2b1 − a1b2)

  • +

+ 6x1x2a2b1(a2b1 − a1b2)ˆ t2 + x1x2a2b1ˆ s2(a2b1 − a1b2 + 6x1x2) + + x1x2ˆ sˆ t

  • (a1b2 − a2b1)2 + a1b2(a1b1 + a2b2) − 2a2b1(2a2b1 + x1b2 + x2a1)
  • w2

= x1x2a2b1

  • 6ˆ

t2(a2b1 − a1b2)2 + 3x1x2a2b1ˆ s2 + ˆ sˆ t(x1b1 + x2a2)(a1b2 − a2b1)

  • V.A. Saleev,Heavy quark jet production at Tevatron in the Regge limit of QCD
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High-energy factorization dσ(p¯ p → X) =

  • i,j

dx1 x1 d2q1T π dx2 x2 d2q2T π Φp

i (x1, t1, µ2)Φ¯ p j(x2, t2, µ2)dˆ

σ(ij → X) dˆ σ(ij → X) = 1 2x1x2S × |M(ij → X)|2 × dΦX At the stage of numerical calculations we use the Kimber-Martin-Ryskin (KMR) prescription for unintegrated quark and gluon distribution functions Φp,¯

p q,g(x, |qT |2, µ2) ,

with the Martin-Roberts-Stirling-Thorne (MRST) collinear densities as input.

V.A. Saleev,Heavy quark jet production at Tevatron in the Regge limit of QCD

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Inclusive jet production at Tevatron, CDF and D0 R + R → g

  • σ/
  • σ/
  • V.A. Saleev,Heavy quark jet production at Tevatron in the Regge limit of QCD
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Inclusive prompt photon production at Tevatron, √ S = 1.8 TeV and √ S = 1.96 TeV, |y| < 0.9, D0 Q + ¯ Q → γ

  • σ/
  • σ/

V.A. Saleev,Heavy quark jet production at Tevatron in the Regge limit of QCD

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Inclusive b−jet production at Tevatron √ S = 1.96 GeV, |yb| < 0.7 Rcone =

  • (yb − y¯

b)2 − (φb − φ¯ b)2 > 0.4

CDF note 8418, 2006, URL: http://www-cdf.fnal.gov/physics/new/qcd/QCD.html

V.A. Saleev,Heavy quark jet production at Tevatron in the Regge limit of QCD

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Inclusive b-jet production

Ratio Data/NLO prediction

jet [GeV/c]

T

P 50 100 150 200 250 300 350 Data / NLO prediction 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Data/NLO prediction (CTEQ6M) corrected at hadron level / 2

b 2

+m

T 2

P =

F

µ =

R

µ Systematic errors NLO uncertainties / 4 (upper)) µ (lower) and µ (scale =0.75

merge

=0.7, f

cone

MidPoint jets, R

  • 1

L ~ 300 pb

∫

= 1.96 TeV, s |Y|<0.7

CDF RunII Preliminary

V.A. Saleev,Heavy quark jet production at Tevatron in the Regge limit of QCD

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  • 8

10

  • 7

10

  • 6

10

  • 5

10

  • 4

10

  • 3

10

  • 2

10

  • 1

10 10

1

d2/dy dpT, nb/GeV 100 200 300 400 50 150 250 350 pT, GeV 1 2

1 - RQb → b, 2 - RR → b¯ b

V.A. Saleev,Heavy quark jet production at Tevatron in the Regge limit of QCD

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Associated b¯ b−jet production at Tevatron √ S = 1.96 GeV, |yb,¯

b| < 1.2, EbT > 35 GeV, E¯ bT > 32 GeV,

Rcone =

  • (yb − y¯

b)2 − (φb − φ¯ b)2 > 0.4

CDF note 8939, 2007, URL: http://www-cdf.fnal.gov/physics/new/qcd/QCD.html.

V.A. Saleev,Heavy quark jet production at Tevatron in the Regge limit of QCD

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b¯ b-pair production

Ratio Data/NLO prediction

(rad) φ ∆

0.5 1 1.5 2 2.5 3

Data/MC

1 2 3 4 5

  • 1

= 1.96 TeV, L = 260 pb s

|<1.2

1.2

η =0.4, |

cone

JetClu R >32 GeV

T,2

>35 GeV, E

T,1

E

CDF Run II Preliminary

  • Syst. uncertainty

Pythia (CTEQ5L) Tune A Herwig (CTEQ5L) + Jimmy MC@NLO (CTEQ6M) + Jimmy

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27 50 100 150 200 250 ET, GeV 10

  • 2

10

  • 1

10 10

1

10

2

d2/d dET, pb/GeV 1 2 3

1 - RR → b¯ b, 2 - Q ¯ Q → b¯ b, 3 - 1+2

V.A. Saleev,Heavy quark jet production at Tevatron in the Regge limit of QCD

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Minv, GeV

10

  • 3

10

  • 2

10

  • 1

10 10

1

10

2

d2/d dMinv, pb/GeV 1 2 3

1 - RR → b¯ b, 2 - Q ¯ Q → b¯ b, 3 - 1+2

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29 1 2 3 0.5 1.5 2.5

, rad

10

1

10

2

10

3

10

4

d2/d , pb/rad 1 2 3

1 - RR → b¯ b, 2 - Q ¯ Q → b¯ b, 3 - 1+2

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Associated b + γ production at Tevatron √ S = 1.96 GeV, |yγ| < 1.0, |yb| < 0.8, 30 < ET γ < 150 GeV, ET b > 15 GeV, Rcone =

  • (yb − yγ)2 − (φb − φγ)2 > 0.7

D0 Collaboration, Phys. Rev. Lett. 102, 192002 (2009).

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40 80 120 160 20 60 100 140 pTγ, GeV 10

  • 6

10

  • 5

10

  • 4

10

  • 3

10

  • 2

10

  • 1

10 d2/dyγ dpTγ, nb/GeV ybyγ>0 5 3 4 2 1

1 - RQb → bγ, 2 - RR → b¯ b(γ), 3 - QQb → bq(γ), 4 - Q ¯ Q → b¯ b(γ), 5 - sum

V.A. Saleev,Heavy quark jet production at Tevatron in the Regge limit of QCD

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40 80 120 160 20 60 100 140 pTγ, GeV 10

  • 6

10

  • 5

10

  • 4

10

  • 3

10

  • 2

10

  • 1

10 d2σ/dyγ dpTγ, nb/GeV ybyγ<0 1 2 3 4 5

1 - RQb → bγ, 2 - RR → b¯ b(γ), 3 - QQb → bq(γ), 4 - Q ¯ Q → b¯ b(γ), 5 - sum

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Associated c + γ production at Tevatron √ S = 1.96 GeV, |yγ| < 1.0, |yc| < 0.8, 30 < ET γ < 150 GeV, ET c > 15 GeV, Rcone =

  • (yc − yγ)2 − (φc − φγ)2 > 0.7

D0 Collaboration, Phys. Rev. Lett. 102, 192002 (2009).

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40 80 120 160 20 60 100 140

pTγ, GeV

10

  • 5

10

  • 4

10

  • 3

10

  • 2

10

  • 1

10

d3/dpTγ dycdyγ, pb/GeV ycyγ >0

1 2 3 4 5

1 - RQc → cγ, 2 - RR → c¯ c(γ), 3 - QQc → cq(γ), 4 - Q ¯ Q → c¯ c(γ), 5 - sum

V.A. Saleev,Heavy quark jet production at Tevatron in the Regge limit of QCD

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35 40 80 120 160 20 60 100 140

pTγ, GeV

10

  • 5

10

  • 4

10

  • 3

10

  • 2

10

  • 1

10

d3/dpTγ dycdyγ, pb/GeV ycyγ <0

1 3 5 4 2

1 - RQc → cγ, 2 - RR → c¯ c(γ), 3 - QQc → cq(γ), 4 - Q ¯ Q → c¯ c(γ), 5 - sum

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Conclusions

  • 1. Within the framework of LO QMRK approach, we have obtained good description

for the inclusive production of single jets, prompt photons, and dijets, containing heavy quarks and photons, in the central rapidity region at Tevatron, without any ad-hoc adjustments of input parameters.

  • 2. The disagreement with the data at the large pT (ET ) or Minv should be explain that

the assumptions of our model don’t work in this kinematical region (x ≥ 0.1)

  • 3. The QMRK approach is once again (*) proven to be a powerful tool for the theoretical

description of QCD processes in the high-energy limit.

V.A. Saleev,Heavy quark jet production at Tevatron in the Regge limit of QCD

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Recent relevant publications

  • 1. Charmonium production: B. A. Kniehl, D. V. Vasin, and V. A. Saleev, Phys. Rev. D 73,

074022 (2006) [arXiv:hep-ph/0602179];

  • 2. Botomonium production: B. A. Kniehl, V. A. Saleev and D. V. Vasin, Phys. Rev. D 74,

014024 (2006) [arXiv:hep-ph/0607254];

  • 3. D meson production: B. A. Kniehl, A. V. Shipilova, and V. A. Saleev, Phys. Rev. D 79,

034007 (2009) [arXiv:0812.3376 [hep-ph]];

  • 4. Prompt photon production: V. A. Saleev, Phys. Rev. D 78, 034033 (2008) [arXiv:0807.1587

[hep-ph]]; V. A. Saleev, Phys. Rev. D 78, 114031 (2008) [arXiv:0812.0946 [hep-ph]]. V. A. Saleev,

  • Phys. Rev. D 80, 114016 (2009) [arXiv:0812.0946 [hep-ph]].
  • 5. b and b + ¯

b production: B. A. Kniehl, A. V. Shipilova, and V. A. Saleev, Phys. Rev. D 81, 094010 (2010) [arXiv:1003.0346 [hep-ph]];

  • 6. γ + jet production: V. A. Saleev, A. V. Shipilova, to be published.

V.A. Saleev,Heavy quark jet production at Tevatron in the Regge limit of QCD