[PPT] - Dirative p ro dution of heavy mesons at the LHC Ma rta PowerPoint Presentation

SLIDE 1 Dira tive p ro du tion

f

heavy mesons at the LHC Ma rta usz zak Institut

f

Physi s Universit y

f

Rzesz w 2-7 June 2016 MESON 2016, Krak

w,

P

land

Ma rta usz zak Universit y

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Rzeszo w

SLIDE 2 Plan

f

the talk Intro du tion Dira tive p ro du tion

f

¯ and b¯ b Hadronization

f

heavy qua rks Dira tive p ro du tion

f
p

en ha rm and b

ttom

Dira tive ha rm p ro du tion within k t

fa to

rization app roa h Con lusions Based

n:

M. usz zak, R. Ma iua and A. Sz zurek, Phys. Rev. D91, 054024 (2015), a rXiv:1412.3132 M. usz zak, R. Ma iua, A. Sz zurek and M. T rzebinski, a pap er in p repa ration Ma rta usz zak Universit y

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SLIDE 3 Intro du tion to dira tive physi s at hadron

lliders

Inelasti dira tive s atterings an b e lassied into three dierent sp e ies.

IP Φ η Φ η η η Φ Φ IP IP IP non−diffractive (ND) single−diffractive (SD) double−diffractive (DD) central−diffractive (CD)

Double Pomeron Exchange (DPE)

Single-dira tion (SD) is the p ro ess initiated b y ex hange

f

p

meron

b et w een intera ting p rotons, whereb y

ne

p roton remains inta t and se ond p roton is destro y ed and p roton remnants app ea r in the dete to r. This b rok en p roton gives rise to a bun h

f

nal pa rti les

r

to a resonan e with the same quantum numb ers. On the side

f

survived p roton a rapidit y gap app ea rs, whi h sepa rate the p roton from remnants. Double-dira tion (DD) is simila rly initiated but here b

th

p rotons do not survive the

llision.

In this ase rapidit y gap is lo ated in the entral rapidit y region. Central-dira tion (CD) alled also Double-P

meron-Ex hange

(DPE) is governed b y p

meron-p
meron

intera tion. Here, b

th
lliding

p rotons remain inta t and some entral system

f

pa rti les, is p ro du ed. In these events t w

utgoing

p rotons a re sepa rated from entral

bje ts

b y t w

rapidit

y gaps. Ma rta usz zak Universit y

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SLIDE 4 Single- and entral-dira tive p ro du tion

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heavy qua rks single- dira tive p ro du tion IP, IR p1 p2 p′ 1 Y X Q ¯ Q g g IP, IR p1 p2 p′ 1 Y X Q ¯ Q qf( ¯ qf) ¯ qf(qf) IP, IR p1 p2 p′ 2 Y X Q ¯ Q g g IP, IR p1 p2 p′ 2 Y X Q ¯ Q ¯ qf(qf) qf(¯ qf) entral- dira tive p ro du tion IP, IR p1 p2 p′ 2 Y2 Y1 Q ¯ Q g p′ 1 IP, IR g IP, IR p1 p2 p′ 2 Y2 Y1 Q ¯ Q ¯ qf(qf) p′ 1 IP, IR qf(¯ qf) leading-o rder gluon-gluon fusion and qua rk-antiqua rk anihilation pa rtoni subp ro esses a re tak en into

nsideration

the extra

rre tions

from subleading reggeon ex hanges a re expli itly al ulated Ma rta usz zak Universit y

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Rzeszo w

SLIDE 5 Theo reti al framew

rk

In this app roa h (Ingelman-S hlein mo del)

ne

assumes that the P

meron

has a w ell dened pa rtoni stru ture, and that the ha rd p ro ess tak es pla e in a P

meronp

roton

r

p rotonP

meron

(single dira tion)

r

P

meronP
meron

( entral dira tion) p ro esses. dσ SD(1) dy 1 dy 2 dp 2 t

=

1 16π 2ˆ s 2 ×

|M

gg→Q ¯ Q| 2 · x 1 g D( x 1, µ 2) x 2 g( x 2, µ 2)

+ |M

q¯ q→Q ¯ Q| 2 ·

x

1 q D( x 1, µ 2) x 2¯ q( x 2, µ 2) + x 1¯ q D( x 1, µ 2) x 2 q( x 2, µ 2)

,

dσ SD(2) dy 1 dy 2 dp 2 t

=

1 16π 2ˆ s 2 ×

|M

gg→Q ¯ Q| 2 · x 1 g( x 1, µ 2) x 2 g D( x 2, µ 2)

+ |M

q¯ q→Q ¯ Q| 2 ·

x

1 q( x 1, µ 2) x 2¯ q D( x 2, µ 2) + x 1¯ q( x 1, µ 2) x 2 q D( x 2, µ 2)

,

dσ CD dy 1 dy 2 dp 2 t

=

1 16π 2ˆ s 2 ×

|M

gg→Q ¯ Q| 2 · x 1 g D( x 1, µ 2) x 2 g D( x 2, µ 2)

+ |M

q¯ q→Q ¯ Q| 2 ·

x

1 q D( x 1, µ 2) x 2¯ q D( x 2, µ 2) + x 1¯ q D( x 1, µ 2) x 2 q D( x 2, µ 2)

,

standa rd

llinea

r MSTW08LO pa rton distributions (A.D. Ma rtin, W.J. Stirling, R.S. Tho rne and G. W att) dira tive distribution fun tion (dira tive PDF) Ma rta usz zak Universit y

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SLIDE 6 Theo reti al framew

rk

The dira tive distribution fun tion (dira tive PDF) an b e

btained

b y a

nvolution
f

the ux

f

p

merons

f I P( x I P) in the p roton and the pa rton distribution in the p

meron,

e.g. g I P(β, µ 2) fo r gluons: g D( x, µ 2) =

dx

I P dβ δ( x − x I Pβ) g I P(β, µ 2) f I P( x I P) =

1

x dx I P x I P f I P( x I P) g I P( x x I P

, µ

2) . The ux

f

P

merons

f I P( x I P) : f I P( x I P) =

t

max t min dt f ( x I P, t) , with t min, t max b eing kinemati b

unda

ries. Both p

meron

ux fa to rs f I P( x I P, t) as w ell as pa rton distributions in the p

meron

w ere tak en from the H1

llab
ration

analysis

f

dira tive stru ture fun tion at HERA. Ma rta usz zak Universit y

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Rzeszo w

SLIDE 7 Results fo r ¯ and b¯ b

(GeV)

t

p

5 10 15 20 25 30

(nb/GeV)

t

/dp σ d

3

10

2

10

1

10 1 10 2 10 3 10 4 10 5 10 6 10

X (SD) c p c → p p = 14 TeV s

gg-fusion (solid)

annihilation (dashed)

q q I P

g

l u

n

I R

g

l u

n

I P

q

u a r k IR-quark = 0.05 G S 2 t = m 2 µ |y| < 8.0

(GeV)

t

p

5 10 15 20 25 30

(nb/GeV)

t

/dp σ d

3

10

2

10

1

10 1 10 2 10 3 10 4 10 5 10 6 10

X (SD) b p b → p p = 14 TeV s

gg-fusion (solid)

annihilation (dashed)

q q I P

g

l u

n

I R

g

l u

n

I P

q

u a r k IR-quark = 0.05 G S 2 t = m 2 µ |y| < 8.0

(GeV)

t

p

5 10 15 20 25 30

(nb/GeV)

t

/dp σ d

3

10

2

10

1

10 1 10 2 10 3 10 4 10

X (CD) c p c → p p = 14 TeV s

gg-fusion (solid)

annihilation (dashed)

q q IP-IP IR-IR IP-IP IR-IR = 0.05 G S 2 t = m 2 µ |y| < 8.0 IP-IR and IR-IP IP-IR and IR-IP

(GeV)

t

p

5 10 15 20 25 30

(nb/GeV)

t

/dp σ d

3

10

2

10

1

10 1 10 2 10 3 10 4 10

X (CD) b p p b → p p = 14 TeV s

gg-fusion (solid)

annihilation (dashed)

q q IP-IP IR-IR IP-IP IR-IR = 0.02 G S 2 t = m 2 µ |y| < 8.0 IP-IR and IR-IP IP-IR and IR-IP the multipli ative fa to rs a re app ro ximately S G = 0.05 fo r single-dira tive p ro du tion and S G = 0.02 fo r entral-dira tive

ne

fo r the nominal LHC energy (√ s = 14 T e V) Ma rta usz zak Universit y

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Rzeszo w

SLIDE 8 Results fo r ¯ and b¯ b

(GeV)

t

p

5 10 15 20 25 30

(nb/GeV)

t

/dp σ d

2

10

1

10 1 10 2 10 3 10 4 10 5 10

X (SD) c p c → p p = 14 TeV s

IP-gluon (solid) IR-gluon (dashed) <0.05 pom x <0.1 pom x < . 1 r e g x <0.2 reg x = 0.05 G S 2 t = m 2 µ |y| < 8.0

(GeV)

t

p

5 10 15 20 25 30

(nb/GeV)

t

/dp σ d

2

10

1

10 1 10 2 10 3 10 4 10 5 10

X (SD) b p b → p p = 14 TeV s

IP-gluon (solid) IR-gluon (dashed) <0.05 pom x <0.1 pom x < . 1 r e g x <0.2 reg x = 0.05 G S 2 t = m 2 µ |y| < 8.0 IP/IR

x

0.05 0.1 0.15 0.2 0.25 0.3 IP/IR

/dx

SD

σ d

4 10 5 10 6 10 7 10

X (SD) c p c → p p = 14 TeV s

IP-gluon (solid) IR-gluon (dashed) = 0.05 G S 2 t = m 2 µ |y| < 8.0 IP/IR

x

0.05 0.1 0.15 0.2 0.25 0.3 IP/IR

/dx

SD

σ d

3 10 4 10 5 10 6 10

X (SD) b p b → p p = 14 TeV s

IP-gluon (solid) IR-gluon (dashed) = 0.05 G S 2 t = m 2 µ |y| < 8.0 in the ase

f

p

meron

ex hange the upp er limit in the

nvolution

fo rmula is tak en to b e 0.1 and fo r reggeon ex hange 0.2 (x I P <

0. 1,

x I R <

0. 2)

the whole Regge fo rmalism do es not apply ab

ve

these limits Ma rta usz zak Universit y

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Rzeszo w

SLIDE 9 Results fo r ¯ and b¯ b

y

8
6
4
2

2 4 6 8

(nb) /dy} σ d

1

10 1 10 2 10 3 10 4 10 5 10

X (SD) c p c → p p X (SD) c p c → p p = 14 TeV s

gg-fusion (solid)

annihilation (dashed)

q q IP-gluon IR-gluon IP-quark IR-quark gluon-IP gluon-IR quark-IP quark-IR = 0.05 G S 2 t = m 2 µ < 30.0 t p

y

8
6
4
2

2 4 6 8

(nb) /dy} σ d

2

10

1

10 1 10 2 10 3 10 4 10

X (SD) b p b → p p = 14 TeV s

gg-fusion (solid)

annihilation (dashed)

q q IP-gluon IR-gluon IP-quark IR-quark gluon-IP gluon-IR quark-IP quark-IR = 0.05 G S 2 t = m 2 µ < 30.0 t p

y

8
6
4
2

2 4 6 8

(nb) /dy} σ d

1

10 1 10 2 10 3 10 4 10 5 10

X (CD) c p p c → p p = 14 TeV s

gg-fusion (solid)

annihilation (dashed)

q q IP-IP sum IR-IR IP-IP IR-IR IP-IR and IR-IP IP-IR and IR-IP = 0.02 G S 2 t = m 2 µ < 30.0 t p

y

8
6
4
2

2 4 6 8

(nb) /dy} σ d

3

10

2

10

1

10 1 10 2 10 3 10

X (CD) b p p b → p p = 14 TeV s

gg-fusion (solid)

annihilation (dashed)

q q IP-IP sum IR-IR IP-IP IR-IR IP-IR and IR-IP IP-IR and IR-IP = 0.02 G S 2 t = m 2 µ < 30.0 t p the individual single-dira tive me hanisms have maxima at la rge rapidities, while the entral-dira tive

ntribution

is

n entrated

at midrapidities. This is a

nsequen e
f

limiting integration

ver

x I P to 0.0 < x I P < 0.1 and

ver

x I R to 0.0 < x I R < 0.2 Ma rta usz zak Universit y

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SLIDE 10 Hadronization

f

heavy qua rks

p1 p2 Q ¯ Q X1 X2

k1,t = 0 k2,t = 0

M ¯ M

hadronization phenomenology → fragmentation fun tions extra ted from e+ e− data

ften

used (older pa rametrizations): P eterson et al., Braaten et al., Ka rtvelishvili et al. mo re up-to-date: ha rm nonp erturbative fragmentation fun tions determined from re ent Belle, CLEO, ALEPH and OP AL data: Knees h-Kniehl-Kramer-S hienb ein (KKKS08) + DGLAP evolution! F ONLL → Braaten et al. ( ha rm) and Ka rtvelishvili et al. (b

ttom)

GM-VFNS → KKKS08 + evolution numeri ally p erfo rmed b y res alling transverse momentum at a

nstant

rapidit y (angle) from heavy qua rks to heavy mesons: dσ( y, p M t ) dyd 2 p M t

≈

D

Q→M( z) z 2

·

dσ( y, p Q t ) dyd 2 p Q t dz where: p Q t = p M t z and z ∈ ( 0, 1) app ro ximation: rapidit y un hanged in the fragmentation p ro ess → y Q = y M Ma rta usz zak Universit y

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SLIDE 11 Predi tions

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integrated ross se tions fo r LHC exp eriments single-dira tion: I R I P+I R ≈ 24 − 31% entral-dira tion: I PI R+I RI P+I RI R I PI P+I PI R+I RI P+I RI R ≈ 42 − 50% single−dira tive non−dira tive

≈

2 − 3% entral−dira tive non−dira tive

≈

0. 03 −
0. 07%

Ma rta usz zak Universit y

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SLIDE 12 k t

fa to

rization in non-dira tive ha rm p ro du tion

p1 p2 Q ¯ Q X1 X2

k1,t = 0 k2,t = 0

k t

fa to

rization −

→ κ

1, t , κ 2, t = Collins-Ellis , Nu l. Phys. B360 (1991) 3; Catani-Ciafaloni-Hautmann, Nu l. Phys. B366 (1991) 135; Ball-Ellis, JHEP 05 (2001) 053

⇒

very e ient app roa h fo r Q Q

rrelations

multi-dierential ross se tion dσ dy 1 dy 2 d 2 p 1,t d 2 p 2,t

=

i,j
d

2κ 1,t

π

d 2κ 2,t

π

1 16π 2( x 1 x 2 s) 2 |M i∗ j∗→ Q ¯ Q| 2

× δ

2

κ

1,t +

κ

2,t − p 1,t − p 2,t

F

i ( x 1, κ 2 1,t ) F j ( x 2, κ 2 2,t)

F

i ( x 1, κ 2 1,t), F j ( x 2, κ 2 2,t)

unintegrated

(k t

dep

endent) gluon distributions LO

-shell |M

g∗ g∗→Q ¯ Q| 2 ⇒ Catani-Ciafaloni-Hautmann (CCH) analyti fo rmulae

r

QMRK app roa h with ee tive BFKL NLL verti es majo r pa rt

f

higher-o rder

rre tions

ee tively in luded

flavour excitation gluon splitting pair creation

with gluon emission

part of the proton hard scattering part of the proton hard scattering hard scattering final state radiation Ma rta usz zak Universit y

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SLIDE 13 Unintegrated gluon distribution fun tions (UGDF s)

log(Q2) BFKL C C F M DGLAP saturation non−perturbative log(1

x)

BK Q

2

= Q

2 S

(x)

most p

pula

r mo dels: Kwie iski, Jung (CCFM, wide range

f

x ) Kimb er-Ma rtin-Ryskin (DGLAP-BFKL, wide range

f

x ) Kwie iski-Ma rtin-Stato (BFKL-DGLAP , small x

values)

Kutak-Stato (BK, saturation,

nly

small x

values)

Lesson from non-dira tive ha rm p ro du tion at the LHC:

(GeV) p

2 4 6 8 10 12 14 16

b/GeV) µ ( /dp σ d

1

10 1 10 2 10 3 10

ALICE

X D → p p = 7 TeV s

| < 0.5

D

|y

MSTW08 = 0.02

c

ε Peterson FF

fact.

t KMR k FONLL NLO PM LO PM

π |/ ϕ ∆ |

0.2 0.4 0.6 0.8 1

) 0.05 π | ( ϕ ∆ /d| σ d σ 1/

0.05 0.1 0.15 0.2 0.25

LHCb

) X D (D → p p = 7 TeV s

< 4.0

D

2.0 < y

2

= m

2

µ = 0.02

c

ε Peterson FF

KMR Jung setA+ KMS

KMR UGDF w

rks

very w ell (single pa rti le sp e tra and

rrelation
bservables)

ma y b e applied fo r ha rd dira tive p ro esses Ma rta usz zak Universit y

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Rzeszo w

SLIDE 14 Mo del fo r dira tive UGDF

fIP(xIP, t) gIP(β, µ2) xIP β =

x xIP

gD(x, µ2)

Resolved p

meron

mo del (Ingelman-S hlein mo del):

nvolution
f

the ux

f

p

merons

in the p roton and the pa rton distribution in the p

meron

b

th

ingredients kno wn from the H1 Collab

ration

analysis

f

dira tive stru ture fun tion and dira tive dijets at HERA First step ⇒ dira tive

llinea

r PDF: g D( x, µ 2) =

dx

I P dβ δ( x − x I Pβ) g I P(β, µ 2) f I P( x I P) =

1

x dx I P x I P f I P( x I P) g I P( x x I P

, µ

2) where the ux

f

p

merons:

f I P( x I P) =

t

max t min dt f ( x I P, t) Se ond step ⇒ dira tive unintegrated gluon within Kimb er-Ma rtin-Ryskin metho d: f D g ( x, k 2 t , µ 2)

≡ ∂ ∂

log k 2 t

g

D( x, k 2 t ) T g ( k 2 t , µ 2)

=

T g ( k 2 t , µ 2) α S( k 2 t ) 2π

×

1

x dz

 

q P gq( z) x z q D x z , k 2 t

+

P gg ( z) x z g D x z , k 2 t

Θ (∆ −

z)

 

T g ( k 2 t , µ 2)

Sudak
v

fo rm fa to r Ma rta usz zak Universit y

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SLIDE 15 Single-dira tive ross se tion

xIP pa pb pa Y X Q ¯ Q β1 x2 Fg(x2, k2

2t, µ2)

FD

g (x1, k2 1t, µ2)

k1t = 0 k2t = 0 t pa pb pb Y X Q ¯ Q β2 x1 xIP FD

g (x2, k2 2t, µ2)

k1t = 0 k2t = 0 t Fg(x1, k2

1t, µ2)

dσ SD(a)( p a p b → p a ¯ XY )

=

dx

1 d 2 k 1t

π

dx 2 d 2 k 2t

π

d ˆ

σ( g∗

g∗ → ¯ ) × F D g ( x 1, k 2 1t, µ 2) · F g ( x 2, k 2 2t, µ 2) dσ SD(b)( p a p b → ¯ p b XY )

=

dx

1 d 2 k 1t

π

dx 2 d 2 k 2t

π

d ˆ

σ( g∗

g∗ → ¯ ) × F g ( x 1, k 2 1t, µ 2) · F D g ( x 2, k 2 2t , µ 2)

F

g a re the

nventional

UGDF s and F D g a re their dira tive

unterpa

rts elementa ry ross se tion with

-shell

matrix element |M g∗ g∗→ ¯ ( k 1, k 2)| 2 inuen e

f

p

meron

transverse momenta

n

initial gluon transverse momenta negle ted, w e assume: gluon k t >> p T

f

p

meron

(o r

utgoing

p roton) Ma rta usz zak Universit y

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SLIDE 16 LO P a rton Mo del vs. k t

fa to

rization app roa h

(GeV)

c T

p

5 10 15 20 25 30

(nb/GeV)

c T

/dp σ d

1 10

2

10

3

10

4

10

5

10

X c p c → p p = 13 TeV s

(single-diffractive)

2

= m

F 2

µ =

R 2

µ = 0.05

G

S IP+IR | < 8

c

|y

factorization (solid)

t

k LO collinear (dashed)

c

y

8
6
4
2

2 4 6 8

(nb)

c

/dy σ d

2

10

3

10

4

10

5

10

6

10

X c p c → p p = 13 TeV s

(single-diffractive)

2

= m

F 2

µ =

R 2

µ = 0.05

G

S IP+IR < 30 GeV

T

p

factorization (solid)

t

k LO collinear (dashed)

signi ant dieren es b et w een LO PM and k t

fa to

rization (simila r as in the non-dira tive ase) higher-o rder

rre tions

very imp

rtant

Ma rta usz zak Universit y

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SLIDE 17 2Dim-distribution in transverse momenta

f

and ¯

(GeV)

1T

p

10 20 30 40 50

(GeV)

2T

p

10 20 30 40 50

4

10

3

10

2

10

1

10 1 10

2

10

3

10

X c p c → p p

(single-diffractive) pomeron

= 13 TeV s (GeV)

1T

p

10 20 30 40 50

(GeV)

2T

p

10 20 30 40 50

4

10

3

10

2

10

1

10 1 10

2

10

3

10

X c p c → p p

(single-diffractive) reggeon

= 13 TeV s

transverse momenta

f
utgoing

pa rti les not balan ed

ne

p t small and se ond p t la rge ⇒

ngurations

t ypi al fo r NLO

rre tions

(in the PM lassi ation) Ma rta usz zak Universit y

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SLIDE 18 Co rrelation

bservables

(GeV)

c c T

p

5 10 15 20 25 30

(nb/GeV)

c c T

/dp σ d

1 10

2

10

3

10

4

10

5

10

X c p c → p p = 13 TeV s

(single-diffractive)

2

= m

F 2

µ =

R 2

µ = 0.05

G

S KMR UGDF IP+IR IP IR | < 8

c

|y

factorization

t

k

(deg)

c c

ϕ

20 40 60 80 100 120 140 160 180

(nb/rad)

c c

ϕ /d σ d

4

10

5

10

X c p c → p p = 13 TeV s

(single-diffractive)

2

= m

F 2

µ =

R 2

µ = 0.05

G

S KMR UGDF IP+IR IP IR | < 8

c

|y

factorization

t

k

quite la rge ¯ pair transverse momenta azimuthal angle

rrelations ⇒

almost at distribution (simila r shap e in the ase

f

in lusive entral dira tion (DPE)) ex lusive entral dira tive events ⇒ smaller p ¯ T and ϕ ¯ mu h mo re

rrelated

(p eak ed at π ) Ma rta usz zak Universit y

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SLIDE 19 Initial gluon vs.

utgoing

p roton transverse momenta

(GeV)

T

proton p

0.5 1 1.5 2

(GeV)

T

gluon k

10 20 30 40 50

2

10

1

10 1 10

2

10

3

10

4

10

X c p c → p p

(single-diffractive) pomeron

= 13 TeV s

the ross se tion

n entrated

in the region

f

p roton p T less than 1 Ge V quite la rge gluon transverse momenta p

meron

p T should not really ae t p redi ted distributions Ma rta usz zak Universit y

f

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SLIDE 20 D meson transverse momentum sp e tra fo r A TLAS

(GeV)

D T

p

5 10 15 20 25 30

(nb/GeV)

D T

/dp σ d

1 10

2

10

3

10

4

10

5

10

X p D → p p X p D → p p = 13 TeV s

(single-diffractive)

2

= m

F 2

µ =

R 2

µ = 0.05

G

S

) = 0.565 D → BR(c

| < 2.1

D

η |

IP+IR IP IR = 0.02

c

ε Peterson FF,

factorization

t

k

KMR UGDF

hadronization ee ts in luded via fragmentation fun tion te hnique (P eterson FF) A TLAS: |η| < 2.1, 0.015 < x IP( x IR) < 0.15 S G = 0.05; BR( → D ) = 0.565 reggeon

ntribution

ma y b e ome mo re imp

rtant

in the fo rw a rd rapidit y region, e.g. in the LHCb dete to r

c

y

8
6
4
2

2 4 6 8

(nb)

c

/dy σ d

2 10 3 10 4 10 5 10 6 10

X c p c → p p = 13 TeV s

(single-diffractive)

2

= m

F 2

µ =

R 2

µ = 0.05

G

S < 30 GeV

T

p

factorization

t

k pomeron (solid) reggeon (dotted)

Ma rta usz zak Universit y

f

Rzeszo w

SLIDE 21 Con lusions The

btained

ross se tions fo r dira tive p ro du tion

f

ha rmed mesons a re fairly la rge and the statisti s seems not to b e any p roblem Rather p

ssible

ba kgrounds and the w a y ho w the dira tive

ntribution

is dened and/o r extra ted is an imp

rtant

issue. W e have p resented a rst appli ation

f

the k t

fa to

rization to ha rd dira tive p ro du tion (very imp

rtant

higher-o rder

rre tions).

Azimuthal angle

rrelation

b et w een and ¯ , and ¯ pair transverse momentum

uld

b e

btained

fo r the rst time. Ma rta usz zak Universit y

f

Rzeszo w