Central exclusive production at RHIC and LHC

Σχετικά έγγραφα
Three coupled amplitudes for the πη, K K and πη channels without data

상대론적고에너지중이온충돌에서 제트입자와관련된제동복사 박가영 인하대학교 윤진희교수님, 권민정교수님

LIGHT UNFLAVORED MESONS (S = C = B = 0)

EPS-HEP 2015 DOUBLE-SCATTERING MECHANISM. Antoni Szczurek 1,2 Mariola Kłusek-Gawenda 1

Approximation of distance between locations on earth given by latitude and longitude

Hadronic Tau Decays at BaBar

Phys460.nb Solution for the t-dependent Schrodinger s equation How did we find the solution? (not required)

derivation of the Laplacian from rectangular to spherical coordinates

HOMEWORK 4 = G. In order to plot the stress versus the stretch we define a normalized stretch:

EE512: Error Control Coding

Lecture 2: Dirac notation and a review of linear algebra Read Sakurai chapter 1, Baym chatper 3

ΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 19/5/2007

Finite Field Problems: Solutions

Higher Derivative Gravity Theories

(1) Describe the process by which mercury atoms become excited in a fluorescent tube (3)

6.1. Dirac Equation. Hamiltonian. Dirac Eq.

Statistical Inference I Locally most powerful tests

CRASH COURSE IN PRECALCULUS

The Simply Typed Lambda Calculus

CHAPTER 25 SOLVING EQUATIONS BY ITERATIVE METHODS

Other Test Constructions: Likelihood Ratio & Bayes Tests

Dong Liu State Key Laboratory of Particle Detection and Electronics University of Science and Technology of China

3.4 SUM AND DIFFERENCE FORMULAS. NOTE: cos(α+β) cos α + cos β cos(α-β) cos α -cos β

2 Composition. Invertible Mappings

Section 8.3 Trigonometric Equations

PARTIAL NOTES for 6.1 Trigonometric Identities

CE 530 Molecular Simulation

Areas and Lengths in Polar Coordinates

the total number of electrons passing through the lamp.

Jesse Maassen and Mark Lundstrom Purdue University November 25, 2013

9.09. # 1. Area inside the oval limaçon r = cos θ. To graph, start with θ = 0 so r = 6. Compute dr

k A = [k, k]( )[a 1, a 2 ] = [ka 1,ka 2 ] 4For the division of two intervals of confidence in R +

Solutions to the Schrodinger equation atomic orbitals. Ψ 1 s Ψ 2 s Ψ 2 px Ψ 2 py Ψ 2 pz

[1] P Q. Fig. 3.1

DESIGN OF MACHINERY SOLUTION MANUAL h in h 4 0.

ANSWERSHEET (TOPIC = DIFFERENTIAL CALCULUS) COLLECTION #2. h 0 h h 0 h h 0 ( ) g k = g 0 + g 1 + g g 2009 =?

Assalamu `alaikum wr. wb.

Capacitors - Capacitance, Charge and Potential Difference

ΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 6/5/2006

ΕΙΣΑΓΩΓΗ ΣΤΗ ΣΤΑΤΙΣΤΙΚΗ ΑΝΑΛΥΣΗ

Mean bond enthalpy Standard enthalpy of formation Bond N H N N N N H O O O

1 String with massive end-points

Space-Time Symmetries

Math 6 SL Probability Distributions Practice Test Mark Scheme

Ordinal Arithmetic: Addition, Multiplication, Exponentiation and Limit

The Θ + Photoproduction in a Regge Model

Right Rear Door. Let's now finish the door hinge saga with the right rear door

Strain gauge and rosettes

Potential Dividers. 46 minutes. 46 marks. Page 1 of 11

Section 7.6 Double and Half Angle Formulas

Derivation of Optical-Bloch Equations

Practice Exam 2. Conceptual Questions. 1. State a Basic identity and then verify it. (a) Identity: Solution: One identity is csc(θ) = 1

measured by ALICE in pp, p-pb and Pb-Pb collisions at the LHC

Matrices and Determinants

Homework 8 Model Solution Section

Dr. D. Dinev, Department of Structural Mechanics, UACEG

b. Use the parametrization from (a) to compute the area of S a as S a ds. Be sure to substitute for ds!

( ) 2 and compare to M.

Every set of first-order formulas is equivalent to an independent set

4.6 Autoregressive Moving Average Model ARMA(1,1)

Fractional Colorings and Zykov Products of graphs

6.3 Forecasting ARMA processes

C.S. 430 Assignment 6, Sample Solutions

Tridiagonal matrices. Gérard MEURANT. October, 2008

The challenges of non-stable predicates

Appendix to On the stability of a compressible axisymmetric rotating flow in a pipe. By Z. Rusak & J. H. Lee

SCHOOL OF MATHEMATICAL SCIENCES G11LMA Linear Mathematics Examination Solutions

TMA4115 Matematikk 3

AdS black disk model for small-x DIS

Bounding Nonsplitting Enumeration Degrees

Reaction of a Platinum Electrode for the Measurement of Redox Potential of Paddy Soil

Numerical Analysis FMN011

An Inventory of Continuous Distributions

Example Sheet 3 Solutions

«ΑΓΡΟΤΟΥΡΙΣΜΟΣ ΚΑΙ ΤΟΠΙΚΗ ΑΝΑΠΤΥΞΗ: Ο ΡΟΛΟΣ ΤΩΝ ΝΕΩΝ ΤΕΧΝΟΛΟΓΙΩΝ ΣΤΗΝ ΠΡΟΩΘΗΣΗ ΤΩΝ ΓΥΝΑΙΚΕΙΩΝ ΣΥΝΕΤΑΙΡΙΣΜΩΝ»

Areas and Lengths in Polar Coordinates

ˆ ˆŠ Œ ˆ ˆ Œ ƒ Ÿ Ä616 Š ˆŒ CMS LHC

ΠΟΛΥΤΕΧΝΕΙΟ ΚΡΗΤΗΣ ΣΧΟΛΗ ΜΗΧΑΝΙΚΩΝ ΠΕΡΙΒΑΛΛΟΝΤΟΣ

Fourier Series. MATH 211, Calculus II. J. Robert Buchanan. Spring Department of Mathematics

ΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 24/3/2007

ST5224: Advanced Statistical Theory II

ΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ. ΘΕΜΑ: «ιερεύνηση της σχέσης µεταξύ φωνηµικής επίγνωσης και ορθογραφικής δεξιότητας σε παιδιά προσχολικής ηλικίας»

Lecture 2. Soundness and completeness of propositional logic

Second Order Partial Differential Equations

What happens when two or more waves overlap in a certain region of space at the same time?

Inverse trigonometric functions & General Solution of Trigonometric Equations

Lecture 34 Bootstrap confidence intervals

SOLUTIONS TO MATH38181 EXTREME VALUES AND FINANCIAL RISK EXAM

Partial Trace and Partial Transpose

department listing department name αχχουντσ ϕανε βαλικτ δδσϕηασδδη σδηφγ ασκϕηλκ τεχηνιχαλ αλαν ϕουν διξ τεχηνιχαλ ϕοην µαριανι

Partial Differential Equations in Biology The boundary element method. March 26, 2013

Econ 2110: Fall 2008 Suggested Solutions to Problem Set 8 questions or comments to Dan Fetter 1

Srednicki Chapter 55

Second Order RLC Filters

Large β 0 corrections to the energy levels and wave function at N 3 LO

Υπολογιστική Φυσική Στοιχειωδών Σωματιδίων

ΖΩΝΟΠΟΙΗΣΗ ΤΗΣ ΚΑΤΟΛΙΣΘΗΤΙΚΗΣ ΕΠΙΚΙΝΔΥΝΟΤΗΤΑΣ ΣΤΟ ΟΡΟΣ ΠΗΛΙΟ ΜΕ ΤΗ ΣΥΜΒΟΛΗ ΔΕΔΟΜΕΝΩΝ ΣΥΜΒΟΛΟΜΕΤΡΙΑΣ ΜΟΝΙΜΩΝ ΣΚΕΔΑΣΤΩΝ

ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΣΧΟΛΗ ΓΕΩΤΕΧΝΙΚΩΝ ΕΠΙΣΤΗΜΩΝ ΚΑΙ ΔΙΑΧΕΙΡΙΣΗΣ ΠΕΡΙΒΑΛΛΟΝΤΟΣ. Πτυχιακή εργασία

Test Data Management in Practice

Transcript:

15th workshop on non-perturbative Quantum Chromodynamics Central exclusive production at RHIC and LHC Antoni Szczurek 1,, Piotr Lebiedowicz 1, Otto Nachtmann 3, 1 Institute of Nuclear Physics PAN Kraków University of Rzeszów 3 Institute für Theoretische Physik, Universität Heidelberg Paris, June 11-13, 18

Our works on central production Our recent works on central production: 1. Production of π + π pairs in pp ppπ + π reaction.. Production of K + K pairs in pp ppk + K reaction. 3. Production of two pairs of π + π in pp ppπ + π π + π reaction Three pomeron exchanges (!) 4. Production of φφ final state pp ppk + K K + K reaction in quest for glueballs 5. Production of p p pairs in pp pp(p p) reaction interesting spin effects for Regge-like reactions. 6. Exclusive production of J/ψ meson in pp ppj/ψ and semiexclusive processes. 7. Production of e + e or µ + µ pairs via γγ fusion with photon transverse momenta. 8. Production of W + W pairs via γγ fusion with photon transverse momenta.

Regge approach At higher energies s > -3 GeV, meson-exchange approach stops to work. Regge approach was proposed. Exchange of so-called Regge trajectories. In the past rather two-body processes were studied. An example is elastic scattering. pp pp, p p p p π + p π + p, π p π p K + p K + p, K p K p Several Regge trajectories are necessary to describe the two-body reactions: (a) leading trajectory (trajectories): pomeron (C=1), odderon (C=-1) (not clearly identified) (b) subleading trajectories: f a (C=+1), ω ρ (C=-1) One can understand total cross sections in the Regge picture. Extension of the Regge approach to 3, 4, etc, processes possible only now. Not yet tested. Use coupling constants extracted from the elastic scattering and total cross sections.

Tensor pomeron model In our recent works all amplitudes are calculated assuming tensor pomeron model proposed by Nachtmann et al., Annals Phys. 34 (14) 31. It is often said that Pomeron has vacuum quantum numbers. This is true for color but not spin degrees of freedom. Often vector pomeron is used in practical calculations. Vector pomeron is inconsistent with Field Theory. Tensor pomeron consistent with so called r 5 observable measured in proton-proton elastic scattering by STAR C. Ewerz, P. Lebiedowicz, O. Nachtmann and A. Szczurek, Phys. Lett. B763 (16) 38. Feynman rules for exchanges of the soft objects have been proposed (vertices, propagators). We keep checking whether it works for different other processes. So far yes! Further tests are needed. Tensor pomeron, see also Chung-I Tan et al. and E. Shuryak et al.

Tensor pomeron The propagator of the tensor-pomeron exchange is written as: i (IP) µν,κλ (s, t) = 1 (g µκ g νλ + g µλ g νκ 1 ) 4s g µνg κλ ( isα IP )αip(t) 1 (1) and fulfils the following relations (IP) µν,κλ (s, t) = (IP) νµ,κλ (s, t) = (IP) µν,λκ (s, t) = (IP) κλ,µν (s, t), g µν (IP) µν,κλ (s, t) =, gκλ (IP) µν,κλ (s, t) =. () It gives by construction the same result for pp pp elastic scattering as traditional Regge approach.

Exclusive reactions Consider exclusive process pp ppm M (pp ppr or even pp ppm MM M) Calculate (helicity-dependent) amplitude M pp ppm M Calculate differential cross sections: dσ = 1 s M pp ppm M (3) (π) 4 δ 4 (p a + p b p 1 p p 3 p 4 ) d 3 p 1 (π) 3 E 1 d 3 p (π) 3 E d 3 p 3 (π) 3 E 3 d 3 p 4 (π) 3 E 4 (4) Any differential distribution can be calculated Include absorption effects

pp ppπ + π p (p a ) p (p 1 ) p (p a ) p (p 1 ) C 1 π + (p 3 ) γ, IP, IR f, f π + (p 3 ) C π (p 4 ) γ, IP, IR π (p 4 ) p (p b ) p (p ) p (p b ) p (p ) The four-body process amplitude written in terms of two-body Regge amplitudes Lebiedowicz, Szczurek, Phys. Rev. D81 () 363.

pp ppπ + π The full Born amplitude of π + π production is a sum of continuum amplitude and the amplitudes through the s-channel resonances: M pp ppπ + π = Mππ continuum pp ppπ + π + M ππ resonances pp ppπ + π. (5) Absorption effects should be included in addition

Resonances Scalar/pseudoscalar resonances: P. Lebiedowicz, O. Nachtmann and A. Szczurek, Ann. Phys. 344C (14) 31. Tensor resonances: q 1 q IP µν IP κλ f ρσ P. Lebiedowicz, O. Nachtmann and A. Szczurek, Phys. Rev. D9 (16) 5415. For tensor meson and tensor pomerons there are 7 possible couplings. We have tried different of them. Only one (!) fits to experimental characteristics.

pp ppπ + π p (p a ) p (p 1 ) t 1 p (p a ) p (p 1 ) t 1 γ, IP, IR γ, IP, IR ˆt π + (p 3 ) π (p 4 ) γ, IP, IR γ, IP, IR û π (p 4 ) π + (p 3 ) t p (p b ) p (p ) t p (p b ) p (p ) The two (t- and u-channel) contributions must be added coherently. P. Lebiedowicz, O. Nachtmann and A. Szczurek, Phys. Rev. D9 (16) 5415.

pp ppπ + π The IPIP-exchange amplitude can be written as where M (IPIP π+ π ) = M (ˆt) λ aλ b λ 1 λ π + π + M (û) λ aλ b λ 1 λ π + π, (6) M (ˆt) λ aλ b λ 1 λ π + π 3β IPNN (p 1 + p a ) µ1 (p 1 + p a ) ν1 δ λ1 λ a F 1 (t 1 )F M (t 1 ) β IPππ (p t p 3 ) µ 1 (p t p 3 ) ν 1 1 4s 13 ( is 13 α IP) α IP(t 1 ) 1 [ˆF π (p t )] p t m π β IPππ (p 4 + p t ) µ (p 4 + p t ) ν 1 4s 4 ( is 4 α IP) α IP(t ) 1 3β IPNN (p + p b ) µ (p + p b ) ν δ λ λ b F 1 (t )F M (t ), (7) M (û) λ aλ b λ 1 λ π + π 3β IPNN (p 1 + p a ) µ1 (p 1 + p a ) ν1 δ λ1 λ a F 1 (t 1 )F M (t 1 ) β IPππ (p 4 + p u ) µ 1 (p 4 + p u ) ν 1 1 4s 14 ( is 14 α IP) α IP(t 1 ) 1 [ˆF π (p u )] p u m π β IPππ (p u p 3 ) µ (p u p 3 ) ν 1 4s 3 ( is 3 α IP )α IP(t ) 1 3β IPNN (p + p b ) µ (p + p b ) ν δ λ λ b F 1 (t )F M (t ). (8)

pp ppπ + π dσ/dm ππ (µb/gev).1.8.6.4 - pp pp π + π s = GeV η < 1, η <, p >.15 GeV π ππ t, π.5 < -t 1, -t <.3 GeV ππ-continuum + f (98) + f (17) j = 1 3 4 ππ-continuum dσ/dm ππ (µb/gev) 1.8.6.4 pp pp π + π η < 1, η π - <, p ππ t, π.3 < -t 1, -t s = GeV >.15 GeV <.3 GeV...5 1 1.5 M ππ (GeV).5 1 1.5 M ππ (GeV) Interesting (negative) interference of f (98) and two-pion continuum.

pp ppπ + π (µb/gev) dσ/dm ππ 1.8.6.4 - p p pp π + π s = 1.96 TeV η < 1.3, y < 1, p >.4 GeV π ππ t, π CDF data..8 1 1. 1.4 1.6 1.8 M ππ (GeV) Not completely exclusive data (protons not measured).

pp ppπ + π (µb/gev) 4 3 pp pp π + π y <, p >. GeV π t, π CMS preliminary data - s = 7 TeV (µb/gev) 4 3 pp pp π + π y <, π p t, π >. GeV CMS preliminary data - s = 7 TeV dσ/dm ππ dσ/dm ππ.5 1 1.5 M ππ (GeV).5 1 1.5 M ππ (GeV) The parameters fixed to the CDF data. Warning: Preliminary CMS data

Photoproduction at HERA VDM (vector dominance model) mechanism: γ ρ [ω] ρ IP, f IR [a IR ] p p Can be inserted to pp collisions.

pp ppπ + π photon induced production of ρ resonances p (p a ) p (p 1 ) p (p a ) p (p 1 ) γ ρ [ω] ρ π + (p 3 ) IP, f IR [a IR ] ρ ρ [ω] π + (p 3 ) π (p 4 ) IP, f IR [a IR ] π (p 4 ) γ p (p b ) p (p ) p (p b ) p (p ) Dominant photoproduction mechanism in the π + π channel. P.Lebiedowicz, O. Nachtmann and A. Szczurek, Phys. Rev. D91 (15) 743.

HERA data p) (µb) σ (γp ρ 5 15 low energy data H1 93 ZEUS 9 ZEUS 93 ZEUS 94 set B set A 5 1 W γp total IP f IR (GeV) 3 No freedom for 4 pp ppρ processes.

pp ppπ + π (µb/gev) dσ/dm ππ 1 IP/IR-IP/IR pp pp π + π s = 7 TeV y <.5 π p >.1 GeV T, π - (µb/gev) dσ/dm ππ 1 IP/IR-IP/IR pp pp π + π s = 7 TeV η <.9 π p >.1 GeV T, π - -1 γ-ip/ir + IP/IR-γ -1 γ-ip/ir + IP/IR-γ -.5 1 1.5 M ππ (GeV) -.5 1 1.5 M ππ (GeV) with absorption effects included

pp ppπ + π photon induced diffractive continuum p (p a) p (p 1) p (p a) p (p 1) p (p a) p (p 1) π (p t) γ π + (p 3) π (p 4) π (p u) γ π (p 4) π + (p 3) γ π + (p 3) π (p 4) IP, f IR IP, f IR IP, f IR p (p b) p (p ) p (p b) p (p ) p (p b) p (p ) So-called Söding mechanism.

Interference effect (µb/gev) dσ/dm ππ 4 3 pp pp π + π s = 7 TeV total ρ (77) continuum interference - -.4.6.8 1 1. 1.4 M ππ (GeV) Modification of the spectral shape (skewdness).

pp ppk + K Purely diffractive resonance mechanisms: p (p a ) p (p 1 ) IP, IR IP, IR f, f K + (p 3 ) K (p 4 ) p (p b ) p (p ) P. Lebiedowicz, O. Nachtmann and A. Szczurek, arxiv:184.476, in print in Phys. Rev. D

pp ppk + K Purely diffractive continuum mechanism: p (p a ) p (p 1 ) t 1 p (p a ) p (p 1 ) t 1 IP, IR IP, IR ˆt K + (p 3 ) K (p 4 ) IP, IR IP, IR û K (p 4 ) K + (p 3 ) t p (p b ) p (p ) t p (p b ) p (p )

pp ppk + K Diffractive photoproduction resonance mechanism: p (p a ) p (p 1 ) p (p a ) p (p 1 ) γ φ φ K + (p 3 ) IP φ φ K + (p 3 ) K (p 4 ) IP K (p 4 ) γ p (p b ) p (p ) p (p b ) p (p )

pp ppk + K Diffractive photoproduction continuum mechanism: p (p a) p (p 1) p (p a) p (p 1) p (p a) p (p 1) K (p t) γ IP, IR K + (p 3) K (p 4) K (p u) γ IP, IR K (p 4) K + (p 3) γ IP, IR K + (p 3) K (p 4) p (p b) p (p ) p (p b) p (p ) p (p b) p (p )

Results for CMS (µb/gev) 1 s = 13 TeV, η, η <.5, p 3 4.17 GeV < p, p y,1,p t,3 t,4 >.1 GeV <.5 GeV y, (µb/gev) 1 pp pp π + π η <.5, p >.1 GeV π t, π - dσ/dm 34 1 dσ/dm ππ -1-3 -3 4 1 1. 1.4 1.6 1.8 M 34 (GeV) -4.5 1 1.5.5 3 M ππ (GeV) CMS rapidity acceptance

Resonance decomposition (µb/gev) dσ/dm 34 1 1 - + pp pp K K s = 13 TeV, η, η < 1. 3 4 total continuum f (98), f (15), f (17) f (17), f (155) 3 4 1 1. 1.4 1.6 1.8 M 34 (GeV) Really many resonances may participate. Parameters fixed by detailed knowledge of different reactions.

f (98) line shape (µb/gev) 8 s = 13 TeV, η, η < 1 3 4 f (98) only m f = 98 MeV = 99 MeV m f (µb/gev) 4 3 s = 13 TeV, η, η < 1 3 4 f (98) only m f = 98 MeV, Γ f = MeV dσ/dm 34 6 4 dσ/dm 34.9.95 1 1.5 1.1 M 34 (GeV).9.95 1 1.5 1.1 M 34 (GeV) left: Γ tot = 7 MeV right: Γ tot = MeV (Achasov-Shestakov) Different position of the peak in π + π and K + K channels. pp ppφ gives contribution at the same M K + K as pp ppf (98) (the first reaction can be smoking-gun for observing effects of gluon saturation)

Angular distribution in the KK rest frame (f (15) and f (17)) (µb) r.f. dσ/dcosθ 3.4.3. s = 13 TeV, η, η < 1., p 3 4 M 34 (1.45, 1.6) GeV total continuum f (155) f (15),p t,3 t,4 >.1 GeV (µb) r.f. dσ/dcosθ 3..15.1 s = 13 TeV, η, η < 1., p 3 4 M 34 (1.65, 1.75) GeV total continuum f (17),p t,3 t,4 >.1 GeV.1.5 1.5.5 1 r.f. cosθ 3 1.5.5 1 r.f. cosθ 3 Not too instructive! Too small range of rapidity? Can CMS measured such distributions?

Angular distribution in the KK rest frame (µb) r.f. dσ/dcosθ 3.1.1.8.6 s = 13 TeV, η, η <.5, p 3 4 M 34 (1.45, 1.6) GeV total continuum f (155) f (15),p t,3 t,4 >.1 GeV.4. 1.5.5 1 r.f. cosθ 3 CMS range of rapidities

Predictions for different experiments (µb/gev) 1 s =. TeV, η, η < 1 3 4 p, p >. GeV t,3 t,4.3 GeV < -t 1, <.3 GeV - π + π (µb/gev) 1 s = 1.96 TeV, CDF data - π + π η, η < 1.3, y < 1 3 4 34 p, p >.4 GeV t,3 t,4 (µb/gev) 1 s = 13 TeV < η, η < 4.5 3 - π + π p, p t,3 4 >. GeV t,4 dσ/dm 34 1 + - K K dσ/dm 34 1 + - K K dσ/dm 34 1 + - K K 3 3 4.8 1 1. 1.4 1.6 1.8 M 34 (GeV) 4.8 1 1. 1.4 1.6 1.8 M 34 (GeV) 3.8 1 1. 1.4 1.6 1.8 M 34 (GeV) Can one observe φ meson?

t t Glueball filter variable distribution dp t = q t,1 q t, = p t, p t,1, dp t = dp t. (9) ) (µb/gev) dσ/d(dp.1.1.8.6 + - pp pp K K, s = 13 TeV η, η < 1, p, p >.1 GeV 4 3 total t,3 t,4 M 34 (1.45, 1.6) GeV continuum f (15) f (155) ) (µb/gev) dσ/d(dp.8.6.4 + - pp pp K K, s = 13 TeV η, η < 1, p, p >.1 GeV 3 4 t,3 t,4 total M 34 (1.65, 1.75) GeV continuum f (17).4....4.6.8 1 (GeV) dp t..4.6.8 1 (GeV) dp t Some difference between continuum and resonances

pp ppπ + π π + π Double resonance production: p p p p IP, IR IP, IR σ σ σ π + π π + π IP, IR IP, IR ρ ρ ρ π + π π + π p p p p

pp ppπ + π π + π Single resonance production: p p p p IP, IR IP, IR f σ σ π + π π + π IP, IR IP, IR f ρ ρ π + π π + π p p p p Contribution to mechanism of diffractive production of resonances (f (17), f 1 (185), f (15), f (17), f (195)) Contribution to decays and branching fractions.

pp ppσσ The amplitude for this process can be written as the following sum: M (σ exchange) pp ppσσ = M (IPIP σσ) + M (IPf IR σσ) + M (firip σσ) + M (f IRf IR σσ) (). For instance, the IPIP-exchange amplitude can be written as M (IPIP σσ) = M (ˆt) λ aλ b λ 1 λ σσ + M(û) λ aλ b λ 1 λ σσ (11) with the ˆt- and û-channel amplitudes M (ˆt) λ aλ b λ 1 λ σσ = ( i)ū(p 1, λ 1 )iγ (IPpp) µ 1 ν 1 (p 1, p a)u(p a, λ a) i (IP) µ 1ν 1,α 1 β 1 (s 13, t 1 ) iγ (IPσσ) α 1 β 1 (p t, p 3 ) i (σ) (p t) iγ (IPσσ) α β (p 4, p t) i (IP) α β,µ ν (s 4, t ) ū(p, λ )iγ µ (IPpp) ν (p, p b )u(p b, λ b ), M (û) λ aλ b λ 1 λ σσ = ( i) ū(p 1, λ 1 )iγ (IPpp) µ 1 ν 1 (p 1, p a)u(p a, λ a) i (IP) µ 1ν 1,α 1 β 1 (s 14, t 1 ) iγ (IPσσ) α 1 β 1 (p 4, p u) i (σ) (p u) iγ (IPσσ) α β (p u, p 3 ) i (IP) α β,µ ν (s 3, t ) ū(p, λ )iγ µ (IPpp) ν (p, p b )u(p b, λ b ). (1) (13)

pp ppρ ρ We write the amplitude as M λaλ b λ 1 λ ρρ = ( ) ( ) ǫ (ρ) ρ 3 (λ 3 ) ǫ (ρ) ρ 4 (λ 4 ) M ρ 3 ρ 4 λ aλ b λ 1 λ ρρ, (14) where ǫ (ρ) ρ (λ) are the polarisation vectors of the ρ meson. M (ρ exchange) ρ 3ρ 4 λ aλ b λ 1 λ ρρ (p 1 + p a) µ1 (p 1 + p a) ν1 δ λ1 λ a F 1 (t 1 ) F M (t 1 ) j V ρ 3ρ 1 µ 1 ν 1 (s 13, t 1, p t, p 3 ) (ρ) ρ 1 ρ (p t) V ρ 4ρ µ ν (s 4, t, p t, p 4 ) hˆfρ(p t )i ff + V ρ 4ρ 1 µ 1 ν 1 (s 14, t 1, p u, p 4 ) ρ (ρ) 1 ρ (p u) V ρ 3ρ µ ν (s 3, t, p u, p 3 ) hˆfρ(p u)i (p + p b ) µ (p + p b ) ν δ λ λ b F 1 (t ) F M (t ), where V µνκλ reads as V µνκλ (s, t, k, k 1 ) =Γ () µνκλ (k 1, k ) 1» 3β IPNN a IPρρ ( isα IP 4s )α IP (t) 1 + 1 g fir pp M a f IR ρρ ( isα f ) α f (t) 1 IR IR Γ () µνκλ (k 1, k ) 1» 3β IPNN b IPρρ ( isα IP 4s )α IP (t) 1 + 1 M g fir pp b f IR ρρ ( isα f IR ) α f IR (t) 1. (15) (16)

σσ and ρ ρ production pp pp(σσ π+π-π+π-) pp pp(ρρ π+π-π+π-) IP and IR -4 4 - -3-3 -4 4 3-4 4 4 Y -4-4 - 4 - -1 - -3 4-1 3 3 - Y Y4 3 IP and IR reggeized s = GeV RY Y 4-1 pp pp(ρρ π+π-π+π-) IP and IR s = GeV RY Y 3 RY Y 4 s = GeV -4-4 - s = GeV Y4 4 - Y 3 - -4-4 - Y4

pp ppπ + π π + π p (p a ) p (p 1 ) p (p a ) p (p 1 ) IP, IR t 1 π + (p 3 ) IP, IR π + (p 3 ) IP, IR t 34 t 45 π (p 4 ) π + (p 5 ) ρ, σ π (p 4 ) π + (p 5 ) IP, IR t 56 t π (p 6 ) IP, IR π (p 6 ) p (p b ) p (p ) p (p b ) p (p ) Only the first type of diagrams was included R. Kycia, P. Lebiedowicz, A. Szczurek and J. Turnau, Phys. Rev. D95 (17) 94.

pp ppπ + π π + π M = 1 ( ) M{3456} + M {5436} + M {3654} + M {5634} + 1 ( ) M{4356} + M {4536} + M {6354} + M {6534} + 1 ( ) M{3465} + M {5463} + M {3645} + M {5643} (17) + 1 ( M{4365} + M {4563} + M {6345} + M {6543} ),

pp ppπ + π π + π M {3456} = A πp(s 13, t 1 ) Fπ(t 34) A ππ(s t 34 mπ 45, t 45 ) Fπ(t 56) A πp(s t 56 mπ 6, t ), (18) M {4356} = A πp(s 14, t 1 ) Fπ(t 43) A ππ(s t 43 mπ 35, t 35 ) Fπ(t 56) A πp(s t 56 mπ 6, t ), (19) M {3465} = A πp(s 13, t 1 ) Fπ(t 34) A ππ(s t 34 mπ 46, t 46 ) Fπ(t 65) A πp(s t 65 mπ 5, t ), () M {4365} = A πp(s 14, t 1 ) Fπ(t 43) A ππ(s t 43 mπ 36, t 36 ) Fπ(t 65) A πp(s t 65 mπ 5, t ). (1)

pp ppπ + π π + π The subprocess amplitudes with the Regge exchanges are given as A πp (s, t) = A ππ (s, t) = j=ip,f IR η j s C j πp j=ip,f IR η j s C j ππ ( s s ( s s ) αj (t) 1 F j πp(t), () ) αj (t) 1 F j ππ(t), (3) where the signature factors are η IP = i and η fir = i.86.

pp ppπ + π π + π dσ [nb/gev] dm 4π 5 4 3 s = 7TeV, ATLAS triple-regge σ 1 1 3 5 15 5 3 M 4π [GeV] Large 4π invariant masses Good measurement for CMS (!) ALICE has too narrow range of rapidities and cannot see it.

pp ppφφ Observed by WA, no theoretical interpretation Two mechanisms possible a priori continuum ("φ" exchange, reggeization (?) ) f (195) (not yet, TTT structure) glueball candidate(s), below (f (17)) and above threshold Let us start exploration, preliminary results below

pp ppφφ, WA data Not yet perfect t (nb/gev) dσ/dm φφ 1 8 6 4 pp pp φφ s = 9.1 GeV WA data φ exchange φ exchange, reggeized Λ off,e = 1.45 GeV ) (nb/gev) dσ/d(dp 15 5 pp pp φφ WA data s = 9.1 GeV φ exchange, reggeized = 1.45 GeV Λ off,e.5 3 3.5 4 M φφ (GeV)..4.6.8 1 dp t (GeV) (nb) pp dσ/dφ 4 3 pp pp φφ WA data s = 9.1 GeV φ exchange, reggeized = 1.45 GeV Λ off,e dσ/d t (nb/gev ) 5 15 pp pp φφ WA data s = 9.1 GeV φ exchange, reggeized = 1.45 GeV Λ off,e 5 5 15 φ (deg) pp..4.6.8 1 t (GeV )

pp ppφφ, predictions for the LHC pp pp(φφ K K K s = 13 TeV η <.5 p (µb) 1 K + - + - K ) >.1 GeV t,k pp pp(φφ K K K s = 13 TeV η <.5 p (µb) 1 K + - - K ) reggeized >.1 GeV + t,k pp pp(φφ K K K s = 13 TeV η <.5 p (µb) 1 K + - - K ) reggeiz >. GeV + t,k dσ/dy 3 dy 4 3 dσ/dy 3 dy 4 3 dσ/dy 3 dy 4 3 4 4 4 Y 3 Y 4 Y 3 Y 4 Y 3

pp ppp p, predictions for the LHC (µb/gev) dσ/dm 4π 1 - - pp pp π + π π + π s = 13 TeV η π <.5, p >.1 GeV t,π η π <.5, p >. GeV t,π η π < 1, p >.1 GeV t,π < η π < 4.5, p >. GeV t,π (µb/gev) dσ/dm 4K 1 3 + - + - pp pp K K K K s = 13 TeV η <.5, p >.1 GeV K t,k η <.5, p >. GeV K t,k η < 1, p >.1 GeV K t,k < η < 4.5, p >. GeV K t,k 1 4 1 3 4 M 4π (GeV) 5.5 3 3.5 4 M 4K (GeV)

pp ppp p, predictions for the LHC (µb) dσ/dy diff 1 - - pp pp π + π π + π s = 13 TeV η π <.5, p >.1 GeV t,π η π <.5, p >. GeV t,π η π < 1, p >.1 GeV t,π < η π < 4.5, p >. GeV t,π (µb) dσ/dy diff 1 3 + - + - pp pp K K K K s = 13 TeV η <.5, p >.1 GeV K t,k η <.5, p >. GeV K t,k η < 1, p >.1 GeV K t,k < η < 4.5, p >. GeV K t,k 1 4 5 3 4 4 Y diff = Y 3 - Y 4 6 4 4 Y diff = Y 3 - Y 4 One should return to the topic once the data at the LHC are available CMS and LHCb data analysis in progress

pp ppp p The continuum (nonresonance) contribution p (p a ) p (p 1 ) t 1 p (p a ) p (p 1 ) t 1 γ, IP, IR γ, IP, IR ˆt p(p 3 ) p(p 4 ) γ, IP, IR γ, IP, IR û p(p 4 ) p(p 3 ) t p (p b ) p (p ) t p (p b ) p (p ) We do Feynman-diagram calculations with well fixed rules (!)

pp ppp p The full amplitude for p p production is a sum of continuum amplitude and the amplitudes with the s-channel resonances: M pp pp pp = M p p continuum pp pp pp + M p p resonances pp pp pp. (4) No p p resonances are known (to us) except of η c and χ c () mesons (see PDG).

pp ppp p M (IPIP pp) λ aλ b λ 1 λ λ 3 λ 4 = ( i)ū(p 1, λ 1 )iγ µ (IPpp) 1 ν 1 (p 1, p a )u(p a, λ a ) i (IP) µ 1ν 1,α 1 β 1 (s 13, t 1 ) ū(p 4, λ 4 )[iγ (IPpp) α β (p 4, p t ) i (p) (p t )iγ (IPpp) α 1 β 1 (p t, p 3 ) + iγ (IPpp) α 1 β 1 (p 4, p u ) i (p) (p u )iγ (IPpp) α β (p u, p 3 )]v(p 3, λ 3 ) i (IP) α β,µ ν (s 4, t ) ū(p, λ )iγ (IPpp) µ ν (p, p b )u(p b, λ b ). No absorption effects. (5)

pp ppp p (µb) dσ/dy 3 3 1-1 s = 13 TeV, no absorption - pp pp π + π + - pp pp K K pp pp pp - - -5 5 y 3 (µb) dσ/dy diff 5 4 3 1-1 - -3-4 s = 13 TeV, no absorption - pp pp π + π + - pp pp K K pp pp pp -6-4 - 4 6 y = y diff 3 - y 4 Surprising effect of the dip at y diff =. New effect for spin-1/ particles Good separation of t and u contributions.

y 3 xy 4 space pp pp π + π s = 13 TeV - pp pp pp s = 13 TeV (µb) 4 (µb) dy 3 1 σ/dy -1 d - 4 dy 3 1 σ/dy -1 d - -3 y 3 5-5 - - -5 5 y 4-3 y 3 5-5 - - -5 5 y 4 Completely different character. The dip is everywhere on the diagonal (ATLAS can do it, ALICE not really).

M p p -distribution (µb/gev) dσ/dm 34 3 1 s = 13 TeV, no absorption - pp pp π + π + - pp pp K K pp pp pp (µb/gev) dσ/dm 34 3 1 s = 13 TeV, no absorption - pp pp π + π + - pp pp K K pp pp pp y, y <.5 3 4-1 -1 - - -3 4 6 8 (GeV) M 34-3 4 6 8 (GeV) M 34 Different slope for pairs of pseudoscalar and for spin-1/ hadrons. We explicitly include spin degrees of freedom in the Regge calculus.

Role of subleading reggeons (µb) dσ/dy 3 3 pp pp pp s = 13 TeV Λ off,e = 1 GeV IP exchange IP, f & a IR exchanges IR (µb) dσ/dy diff 3 pp pp pp s = 13 TeV Λ off,e = 1 GeV IP exchange IP, f & a IR exchanges IR 1 1-1 -1 - - -5 5 y 3 - -4-4 y = y diff 3 - y 4 Even at s = 13 TeV a sizeable effect of subleading reggeons.

M p p xy diff pp pp pp s = 13 TeV (µb/gev) diff σ/dm 34 dy d M 34 1-1 - (GeV) 5 5 y diff -5 Region inside of the ridge seems promissing in searches for resonances

π + π versus p p production (GeV) M 34 8 6 - pp pp π + π s = 13 TeV, d σ/dm 34 dy (µb/gev) diff 1 (GeV) M 34 pp pp pp s = 13 TeV, d σ/dm 34 dy (µb/gev) diff 8 6 1 4-1 4-1 - - -4-4 y diff -3-4 - 4 y diff -3 Different situation for π + π and p p

Potential role of resonances with M GeV (µb) dσ/dy diff.5.4.3 s = 13 TeV, no absorption pp pp pp, Λ off,e =.8 GeV η, η <.5 3 4 p, p >.1 GeV t,3 t,4 total continuum f ()..1-4 - 4 y = y - y diff 3 4 resonances may distroy the dip

Potential role of resonances with M GeV (GeV) M 34 pp pp pp s = 13 TeV, d σ/dm 34 dy 3.5 3 diff (µb/gev) 1-1.5-1.5 η, η <.5 3 4 p, p >.1 GeV t,3 t,4 - -1 1 y diff -3-4 resonances may distroy (close) the gorge

Role of ingredients, ratios 3 η pp pp pp s = 13 TeV R 6 (IP + IR) (η 3, η ) 4 3 η pp pp pp s = 13 TeV R 6 (IP + IR + O) (η 3, η ) 4 1.1 4 LHCb 1.8 1.6 4 LHCb 1.5 1 4 ATLAS 1.4 1. 4 ATLAS.995 6 6 4 4 6 η 4 1 6 6 4 4 6 η 4.99 first: role of subleading reggeons second: role of odderon

Asymmetry between central p and p In two dimensions (e.g. η 1 η ) we can define the asymmetry: Ã () (η,η ) = d σ dη 3 dη 4 (η,η ) d σ dη 3 dη 4 (η,η) d σ dη 3 dη 4 (η,η ) + d σ dη 3 dη 4 (η,η). (6)

Asymmetry between central p and p A = σ(p) σ( p) σ(p) + σ( p) (7) η pp pp pp s = 13 TeV 6 A ~ () (η, η ).15 4.1 LHCb.5 4 ATLAS.5.1 6 6 4 4 6 η.15 Clear asymmetry

Asymmetry between central p and p Projection on one-dimension (full phase space) (η) A pp..1 pp pp pp, s = 13 TeV Λ off,e = 1 GeV -.1 -. -5 5 η

Asymmetry between central p and p Projection on one-dimension (experimental cuts) (η) A pp..1 pp pp pp, s = 13 TeV ATLAS kinematics Λ off,e = 1 GeV (η) A pp.1.5 pp pp pp, s = 13 TeV LHCb kinematics Λ off,e = 1 GeV.1 -.5. 1 1 η -.1.5 3 3.5 4 4.5 η

Conclusions, pp pph + h The Regge phenomenology was extended in practice to 3, 4 and 6 exclusive processes. The tensor pomeron/reggeon model was applied to many reactions. At lower energies tensor/vector reggeons. The dipion invariant mass has a rich structure which strongly depends on kinematical cuts (continuum, resonances, interference). Disagreement with CMS data due to large dissociation contribution. Purely exclusive data expected from STAR, CMS+TOTEM and ATLAS+ALFA.

Conclusions, pp pph + h K + K has also rich invariant mass structure (resonances). Predictions have been done. Some ambiguities in predictions. Search for glueballs requires partial wave analyses and observations in different final states. Four-pion production is also interesting. Double resonances, three-pomeron continuum. Search for single resonances (f (17)). φφ (K + K K + K ) final state at s = 9.1 GeV has been approximately described including continuum contribution. Predictions for LHC were shown. Resonances (glueballs) should be added. p p production has quite different characteristics (dσ/dm and dσ/dy diff (dip)). These are predictions of our approach.

2025 © DocPlayer.gr Πολιτική Απορρήτου | Όροι Χρήσης | Σχόλια