Pomeron Physics at the LHC

Emerson Luna

Federal University of Rio Grande do Sul

XXXIX Encontro Nacional de Física

de Partículas e Campos

Campos do Jordão, Brazil, 2018

XXXIX ENFPC Campos do Jordão, 25 September 2018

Introduction

The Pomeron was introduced to describe diffractive processes

⇒ include elastic scattering, single- or double- diffractive

dissociation, double Pomeron exchange, ...

⇒ are characterized by the presence of one or more large

rapidity gaps (LRG):

⇒ LRGs are associated with the exchange of a colorless state

having the quantum numbers of the vacuum: the Pomeron

XXXIX ENFPC Campos do Jordão, 25 September 2018

Why study the Pomeron (Diffraction)?

In pp collisions at LHC about 40% of σtot comes from

diffractive processes

In pp collisions there is a very large probability for additional

soft interactions of the spectator partons that accompany the

partons of the main subprocess of interest ...

... study of the Pomeron needed to understand the nature of

these underlying events

⇒ a LRG can be filled by debris originated from the

rescattering of spectator partons ...

... study of the Pomeron needed to estimate the survival

probabilities of LRGs to soft rescattering

XXXIX ENFPC Campos do Jordão, 25 September 2018

The systematic analyses of LRGs open the possibility of

extracting New Physics from hard diffractive processes

⇒ see for example the exclusive Higgs boson production

pp → p ⊕ H ⊕ p

⇒ it may be possible to measure MH to high precision

⇒ this precision would then enhance the signal over the

continuum background (for example in the H → bb channel)

The study of diffraction may allow the construction of a

theory which merges soft and hard high-energy (HE) hadron

interactions in a reliable and consistent way

Studies of diffractive processes should help in understanding

the structure of high energy cosmic ray phenomena

XXXIX ENFPC Campos do Jordão, 25 September 2018

The Pomeron in the S-matrix theory

The Pomeron was introduced in the framework of the

complex angular momentum theory

In the soft regime, i. e. small t domain, diffractive processes

are described by Regge theory:

⇒ the HE behavior of the scattering amplitude is described by

singularities of the amplitude in plane j

⇒ the relativistic partial wave amplitude Aj(t) can be

analytically continued to complex j values in a unique way

⇒ in the simplest scenario the resulting function A(j , t) has

simple poles at

j = α(t) (1)

XXXIX ENFPC Campos do Jordão, 25 September 2018

The Pomeron in the S-matrix theory

⇒ as a result we have an elastic amplitude A(s, t) written in

terms of the Regge pole trajectory α(t):

A(s, t) ∝ sα(t) (2)

If more than one pole contributes, A(s, t) is expressed as

A(s, t) =∑

i

γi(t)ηi(t)sαi (t), (3)

where γi(t) is the residue function and ηi(t) is the signature

factor

⇒ from the unitarity relation sσtot(s) = 4πImA(s, t = 0), the

total cross section reads

σtot(s) =∑

i

4πgisαi (0)−1, gi ≡ γi(0)Imηi(0) (4)

XXXIX ENFPC Campos do Jordão, 25 September 2018

The Pomeron in the S-matrix theory

Thus the leading singularity (i.e. the singularity with the

largest real part) in the t-channel determines the asymptotic

behavior of A(s, t) in the s-channel

⇒ the Pomeron is the pole with the largest intercept, originally

αP(0) = 1

⇒ the magnitude of its intercept plays a central role in Regge

theory

⇒ general unitarity arguments constrain the physical Pomeron

intercept, αP(0) ≤ 1

The Pomeron as it emerges from fits to forward (t ≈ 0)

observables is called soft Pomeron

XXXIX ENFPC Campos do Jordão, 25 September 2018

The modern viewpoint: Reggeon Field Theory

However, in order to describe the observed increase of all

hadronic σtot(s) at HE, the Pomeron should have an effective

intercept such that αP(0) = 1 + ǫ with ǫ > 0

⇒ This supercritical intercept value is arrived at by taking into

account, in addition to Regge poles, multi-Pomeron cuts in the

j-plane

⇒ Reggeon Field Theory (RFT) enables one to systematically

analyze the exchange of poles and branch points in HE scatt.

⇒ RFT is first motivated by a consideration of hybrid Feynman

graphs

⇒ rules for Reggeon interaction and propagation are

formulated

⇒ the bare Pomeron intercept may be greater than one

XXXIX ENFPC Campos do Jordão, 25 September 2018

The modern viewpoint: Reggeon Field Theory

In RFT the elastic and low-mass diffractive dissociation are

described in terms of a multi-channel eikonal

The high-mass diffraction is described in terms of diagrams

with multi-Pomeron couplings

⇒ the processes pp → pX with large MX are usually described

in terms of a triple-Regge formalism, where

M2X ≃ (1 − xL)s (5)

where

xL ≡ 1 − ξ (6)

is the momentum fraction of the ingoing proton carried by the

outgoing proton

XXXIX ENFPC Campos do Jordão, 25 September 2018

The modern viewpoint: Reggeon Field Theory

Hence the excitation into higher mass MX states is described

by the triple-Pomeron graph

Since we have large MX we no longer have −t = q2; rather we

must allow for non-vanishing tmin

−t =q2

xL=

m2p(1 − xL)

2

xL=

q2

xL− tmin (7)

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Soft Diffraction at LHC: a multi Pomeron approach

We now have all the ingredients for building a model for the

Pomeron. Unfortunately, however, ...

... no way has been found to sum up all the Regge graphs

and to solve Regge Field Theory

We developed a model of the Pomeron which, at the very least,

accounts for the most important effects

XXXIX ENFPC Campos do Jordão, 25 September 2018

Soft Diffraction at LHC: a multi Pomeron approach

We have incorporated into our model [1,2]:

• s-channel unitarity with elastic and a low mass MX

intermediate state by using a two-channel eikonal approach

• the two-pion loop, the nearest t-channel singularity

• high-mass MX single- and double- dissociation

• screening corrections in the triple-Regge formalism

⇒ in particular, we allow for the gap survival probability in

single proton diffractive dissociation

[1] E.G.S. Luna, V.A. Khoze, A.D. Martin, M.G. Ryskin, Eur. Phys. J. C59

(2009) 1

[2] E.G.S. Luna, V.A. Khoze, A.D. Martin, M.G. Ryskin, Eur. Phys. J. C69

(2010) 95

XXXIX ENFPC Campos do Jordão, 25 September 2018

The Model

In our model the Born level amplitude is written as

ABorn(s, t) = AIP(s, t) +Aa/f (s, t) + τAω/ρ(s, t)

and the opacity (or eikonal) Ω(s, b) is given by

Ω(s, b) =2

s

∫

∞

0

q dq J0(bq)ABorn(s, t).

The Pomeron contribution is given by

AIP(s, t) = iβ2IP(t)

(

s

s0

)αIP(t)

,

αIP(t) = α(0) + α′t +β2πm2

π

32π3h

(

4m2π

|t |

)

(8)

⇒ last term generated by t-ch unitarity ⇒ pion-loopinsertions

XXXIX ENFPC Campos do Jordão, 25 September 2018

The eikonalized amplitude is given by:

A(s, t) = is

∫

∞

0

b db J0(bq)

[

1 −e−

Ω2(1+γ)2

4−

e−Ω2(1−γ2)

2

−e−

Ω2(1−γ)2

4

]

,

where γ = 0.55 ⇒ s-ch unitarity with elastic and a low mass

M2 intermediate state via a 2-ch eikonal approach (using a

representative effective low mass proton excitation N∗)

The total and elastic cross section are given by

σtot(s) =4π

sImA(s, t = 0),

dσel

dt(s, t) =

π

s2|A(s, t)|2.

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Screening Corrections

The triple-Pomeron vertex g3IP(t) is a central ingredient for

understanding diffraction:

⇒ its coupling and t-dependence determine the asymptotic HE

behavior of total cross sections and the cross section of

diffractive dissociation

⇒ the calculation of the rapidity gap survival factors S2

depends on the properties of g3IP(t)

In the triple-Regge description of high mass diffractive

dissociation we have

M2 dσ

dtdM2= βj(0)β

2i (t)giij(t)

( s

M2

)2αi (t)−2(

M2

s0

)2αj (0)−1

XXXIX ENFPC Campos do Jordão, 25 September 2018

Screening Corrections

To determine the t dependence we take the Fourier

transforms with respect to the impact parameter:

M2 dσ

dtdM2= A

∫

d2b2

2πei~qt ·

~b2Fi(b2)

∫

d2b3

2πei~qt ·

~b3Fi(b3)

∫

d2b1

2πFj(b1) (9)

where

Fi(b2) =1

2πβi

∫

d2qtβi(qt)( s

M2

)−α′

iq2

t

e−b′

iijq2

t ei~qt ·~b2 ,

Fj(b1) =1

2πβj

∫

d2ktβj(kt)

(

M2

s0

)−α′

jk2

t

e−b′

iijk2

t ,

A = βj(0)β2i (0)giij(0)

( s

M2

)2αi (0)−2(

M2

s0

)αj (0)−1

.

XXXIX ENFPC Campos do Jordão, 25 September 2018

To calculate screening corrections we must include in the

integrands on the right-hand side of (9) the factors

exp(−Ω(~b2 + ~b1)

2) exp(−

Ω(~b3 + ~b1)

2) ≡ S(~b2 + ~b1)S(~b3 + ~b1)

⇒ that is, we need to compute

M2 dσ

dtdM2

∣

∣

∣

∣

iij

= A

∫

d2b1

2πFj(b1)|Id(b1)|

2

where

Id(b1) ≡

∫

d2b2

2πei~qt ·

~b2 Fi(b2)Si(~b2 + ~b1).

⇒ the generalization to a two-ch eikonal takes into account the

Pomeron couplings to each diffractive eigencomponent k to be

βIP,k (t) = (1 ± γ)βIP(t)

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Determination of the Triple-Pomeron vertex

first step: global fit to total and differential cross sections ⇒model including low mass diffraction, pion loop insertions

in the Pomeron trajectory, and rescattering effects via a

two-channel eikonal

second step: generalization of screening calculations to a

two-channel eikonal ⇒ large expressions ⇒ hard

computational task

third step: triple-Regge analysis of pp → pX data ⇒ all the

screened effects included ⇒ determination of the

triple-Pomeron coupling g3IP(0)

⇒ it is important to distinguish between the weak and strong

triple-Pomeron coupling behaviors

XXXIX ENFPC Campos do Jordão, 25 September 2018

Determination of the Triple-Pomeron vertex

The energy behaviour of the scattering amplitude may be

consistently described by two different scenarios for the

asymptotic regime ⇒ weak × strong IP-couplings

In the weak coupling scenario σtot tends to the universal

constant value: σtot → constant as s → ∞

⇒ in order to not violate unitarity g3IP ∝ q2t as q2

t → 0

In the strong coupling scenario the cross section grows as

σtot ∝ (ln s)η with qt → 0

⇒ in this case the bare vertex g3IP |qt→0 → constant

⇒ we see from a χ2 analysis that the data clearly prefer the

strong triple-Pomeron coupling

XXXIX ENFPC Campos do Jordão, 25 September 2018

Figure I: The description of a sample of the d2σ/dtdξ cross section data that

are fitted using the strong (continuous curves) and weak (dashed curves)

triple-Pomeron coupling ansatzes (ξ ≃ M2/s).

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Figure II: The description of the CERN-ISR pp → pX cross section data

obtained in the strong triple-Pomeron coupling scenario.

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Figure III: The description of the d2σ/dtdξ, measured in fixed-target and

collider experiments at FNAL (strong triple-Pomeron coupling scenario).

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Figure IV: The t-dependence of the d2σ/dtdξ at ξ = 0.02, 0.06 and s = 550

GeV2 obtained in the strong and weak triple-Pomeron fits.

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Figure V: The t-dependence of the d2σ/dtdξ at ξ = 0.01, 0.1 and√

s = 1800

GeV obtained in the strong and weak triple-Pomeron fits.

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Figure VI: The continuous curves are the predictions for the t-dependence of

the d2σ/dtdξ at ξ = 0.01, 0.1 and√

s = 14 TeV in the strong triple-Pomeron

fit. The disfavoured weak coupling predictions are shown by dashed curves.

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Figure VII: Description of total cross section and ρ parameter data.

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Figure VIII: Description of differential cross section data from TOTEM.

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Figure IX: Description of differential cross section data from ATLAS.

XXXIX ENFPC Campos do Jordão, 25 September 2018

Inelastic J/ψ Photoproduction

The process γp → J/ψ + Y at large values of MY offers, in

principle, an opportunity to determine the triple-Pomeron

coupling where the screening corrections are smaller than in

the pure hadronic reactions

Figure VII: The process of proton dissociation in diffractive J/ψ

photoproduction, γp → J/ψ + Y , which is described by a diagram with a

triple-Pomeron vertex in which the rescattering effects are small. The dotted

line would mean the diagram became an enhanced diagram.

⇒ unfortunately the M2Y distribution has not measured yet...

XXXIX ENFPC Campos do Jordão, 25 September 2018

However there exists a comparison of the HERA data for the

“elastic” photoproduction process, γp → J/ψ + p with the

proton dissociation data

⇒ the ratio, at the pp centre-of-mass energy W = 200 GeV

and t = 0 is (ZEUS, H1):

r ≡dσ(γp → J/ψ + Y )/dt

dσ(γp → J/ψ + p)/dt≃ 0.2, (10)

where the “inelastic” cross section has been integrated over the

mass region MY < 30GeV .

Our analysis gives r = r3IP + rIPIPIR = 0.12 + 0.06

⇒ this result is consistent with HERA data, within the

uncertainties.

XXXIX ENFPC Campos do Jordão, 25 September 2018

In our formalism

r3IP =g3IP

πβIP

∫

dM2

M2

(

W 2

M2

)2αIP−2 (M2

s0

)2αIP(0)−1

rIPIPIR =gIPIPIR

πβIP

∫

dM2

M2

(

W 2

M2

)2αIP−2 (M2

s0

)2αIR(0)−1

⇒ here αIP(0) is the usual “soft” Pomeron

⇒ αIP include DGLAP evolution from a low initial scale µ = µ0

up to a rather large scale µ = MJ/ψ at the J/ψ production vertex

⇒ the summation of double logarithms (αs ln(1/x) ln(µ2/µ20))

n

leads to a steeper x-dependence and hence to a larger

effective intercept → we adopt αIP = 1.18, which corresponds

to the W dependence observed in the HERA data

XXXIX ENFPC Campos do Jordão, 25 September 2018

Concluding Remarks

We have described a global analysis of available pp and pp

in CERN-ISR to LHC energy range

First triple-Pomeron analysis including screening corrections

⇒ absorptive effects depend on the energy

We have obtained g3IP(0) = 0.44 ± 0.06 GeV−1

⇒ we can use this result to predict the diffractive effects at the

LHC

⇒ this coupling is supported by an analysis of J/ψphotoproduction data measured at HERA

⇒ g3IP(0) value consistent with the reasonable extrapolation of

the perturbative BFKL Pomeron vertex to the low scale region

XXXIX ENFPC Campos do Jordão, 25 September 2018

Concluding Remarks

The triple-Pomeron vertex turns out to be rather large,

g3IP ≃ 0.2β3IP

⇒ this indicates that we must include more complicated

‘enhanced’ diagrams

We found that the data prefer the strong Pomeron coupling

scenario

⇒ it will be important to measure the inclusive cross section for

single diffraction, d2σ/dtdξ, at the LHC to confirm this

conclusion

⇒ this could be done when the forward detectors are operating

at the LHC, even at moderate integrated luminosity

XXXIX ENFPC Campos do Jordão, 25 September 2018

Concluding Remarks

We note that our analysis of the data prefers zero slopes,

corresponding to small size of the bare triple-Reggeon vertices

Soft-hard transition emerges:

⇒ “soft” compt. → heavily screened → little growth with s

⇒ “intermediate” compt. → some screening

⇒ “hard” compt. → little screening → large growth with s (∼pQCD)

⇒ this behavior gives hope that there is a smooth matching to

the perturbative QCD treatment of the Pomeron

XXXIX ENFPC Campos do Jordão, 25 September 2018

THANK YOU

XXXIX ENFPC Campos do Jordão, 25 September 2018