bridging high and low scale physics in effective field … · 2019. 12. 4. · eft and lhc physics...

BRIDGING HIGH AND LOW SCALE PHYSICS IN  EFFECTIVE FIELD THEORIES AND APPLICATIONS TO  LHC PHYSICSHEE SOK CHUNG T30F GROUP,  WITH PROF. BRAMBILLA AND PROF. VAIROORIGINS SCIENCE WEEK 2019

EFT AND LHC PHYSICS

EFFECTIVE FIELD THEORIES AND QCD▸ To our best knowledge, the law of nature governing strong

interaction is given by quantum chromodynamics (QCD) that describes interaction between quarks and gluons.

▸ QCD changes its appearance according to distance scales :  strong interaction becomes stronger at long distances.  Hence, quarks and gluons evolve into stable particles through low energy interactions before they can be measured.

▸ Theoretical predictions of measurements at the LHC must encompass not only the high-energy process of quarks and gluons but also the low-energy process where quarks and gluons evolve into observed particles.

Origins Science Week 2019 Hee Sok Chung

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EFT AND LHC PHYSICS

EFFECTIVE FIELD THEORIES AND QCD▸ EFTs provide formalisms that separate the high- and low-energy

physics.

▸ It is well-known how to compute the high-energy part : the QCD interaction becomes weak, so we can use perturbation theory.

▸ It is not so well known how to compute the low-energy part. QCD interaction becomes so strong, that perturbation theory is invalid.

▸ One of the biggest challenges in QCD is to understand the nonperturbative low-energy part from first principles. EFTs can organize the nonperturbative physics into a limited number of nonperturbative parameters.


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EFT AND LHC PHYSICS

HEAVY QUARKONIUM▸ We use the simplest nonperturbative system to better

understand the nonperturbative aspects of QCD.

▸ Heavy quarkonia are bound states of a heavy quark Q and antiquark Q̅ (Q = c or b).  The Q and Q̅ move slowly inside the bound state, so we can use nonrelativistic approximations.

▸ Using EFT methods, separating scales above and below the heavy quark mass m gives us nonrelativistic QCD (NRQCD). In NRQCD, observables are given in an expansion in powers of the heavy-quark velocity v.


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EFT AND LHC PHYSICS

NONRELATIVISTIC QCD▸ NRQCD provides a description of a heavy quarkonium

state as    v2≈0.3 for charmonia (bound states of cc̄),  v2≈0.1 for bottomonia (bound states of bb̄).

▸ NRQCD have been successfully applied to explain spectroscopy and decay processes.

▸ Application of NRQCD to production processes of heavy quarkonia at LHC has been a challenge.


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Caswell, Lepage, PLB167, 437 (1986) Bodwin, Braaten, Lepage, PRD51, 1125 (1995),  

PRD55, 5853 (1997)

EFT AND LHC PHYSICS

PRODUCTION IN NRQCD▸ Production rate of a heavy quarkonium H in a high-energy

collision (energy much larger than the quarkonium mass) is given by   n : spin and color state of QQ̅  σQQ̅(n) : perturbative cross section of QQ̅  ⟨𝓞n⟩H : nonperturbative matrix element, describes evolution   of QQ̅ in state n to evolve into quarkonium H.

▸ The series can be truncated to desired accuracy in v. NRQCD organizes the nonperturbative physics into a few real numbers ⟨𝓞n⟩H.


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Bodwin, Braaten, Lepage, PRD51, 1125 (1995),  PRD55, 5853 (1997)

σH = ∑n σQQ̅(n) ×⟨𝓞n⟩H

EFT AND LHC PHYSICS


collision  

▸ The σQQ̅(n) can be computed in perturbative QCD, by calculating Feynman diagrams.  A few representative diagrams :


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…++

EFT AND LHC PHYSICS


collision  

▸ With the exception of a few known cases, it is not known to compute the ⟨𝓞n⟩H from first principles. So, in existing studies, the ⟨𝓞n⟩H are obtained by comparing σH with data.

▸ The ⟨𝓞n⟩H extracted from measurements depend strongly on the choice of data, which also affects predictions strongly.

▸ Determination of ⟨𝓞n⟩H from QCD is the biggest challenge in predicting heavy quarkonium production rates at the LHC.


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EFT AND LHC PHYSICS

POTENTIAL NRQCD▸ A heavy quarkonium system has two distinct scales below m :

momentum mv and kinetic energy mv2.

▸ Separating mv and mv2 leads to a new EFT called potential NRQCD (pNRQCD), where the Q and Q̅ interact nonrelativistically via a known potential.

▸ In pNRQCD, description of a heavy quarkonium system becomes a nonrelativistic quantum mechanics problem,  like solving the Schrödinger equation for the hydrogen atom.

▸ Higher order corrections can be included systematically, which involve low-energy gluons interacting with gluons and also with the Q and Q̅.


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Brambilla, Eiras, Pineda, Soto, Vairo, PRD 67, 034018 (2003)

EFT AND LHC PHYSICS

PRODUCTION OF AT LHC▸ We applied pNRQCD methods to compute production of

𝜒bJ(nP) at the LHC (J=0,1,2 and n = 1,2,3). The production rate of 𝜒bJ(nP) at leading order in v is given by

▸ For each n, two nonperturbative matrix elements are necessary to make predictions of production rates.  While it is known how to compute ⟨𝓞 ⟩ ,  it is not known how to compute ⟨𝓞 ⟩ .


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𝜒bJ(nP)

σ = (2 J+1) [ σ ×⟨𝓞 ⟩ 𝜒bJ(nP) QQ̅(3PJ[1]) (3P0[1]) 𝜒bJ(nP) +σ ×⟨𝓞 ⟩ ]QQ̅(3S1[8]) (3S1[8]) 𝜒bJ(nP)

(3P0[1]) 𝜒bJ(nP)

(3S1[8]) 𝜒bJ(nP)

EFT AND LHC PHYSICS

PRODUCTION OF AT LHC▸ ⟨𝓞 ⟩ is sensitive to the bb̄ component of the

quarkonium. In pNRQCD, this state is just given by b and b̄ interacting through a potential, and can be described by solving the Schrödinger equation. Then,     where RnP(r) is the radial wavefunction from the solution of the Schrödinger equation, with orbital angular momentum 1, and radial excitation n.


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𝜒bJ(nP)(3P0[1]) 𝜒bJ(nP)

⟨𝓞 ⟩ (3P0[1]) 𝜒bJ(nP)

EFT AND LHC PHYSICS

PRODUCTION OF AT LHC▸ ⟨𝓞 ⟩ is sensitive to the bb̄g component of the

quarkonium. It has not been known how to compute this matrix element.

▸ By a careful analysis using NRQCD and potential NRQCD, we have found that the small radius of the bottomonium systems allow us to separate the interaction of the bb̄ and the low-energy gluons, so that    where R8 is a universal constant in QCD that is determined by the behavior of low-energy gluons in vacuum, and does not depend on the specific 𝜒bJ(nP) state.


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𝜒bJ(nP)

⟨𝓞 ⟩ 𝜒bJ(nP)

(3S1[8]) 𝜒bJ(nP)

(3S1[8])

EFT AND LHC PHYSICS

PRODUCTION OF AT LHC

▸ RnP(r) are determined from the Schrödinger equation.  So the production rates of 𝜒bJ(nP) (J=0,1,2 and n=1,2,3) are determined by a single universal parameter R8 defined in QCD by

▸ We determined R8 from decay widths of 𝜒cJ(1P), where R8 also appears. In the future, we plan to compute R8 from first principles by using lattice QCD.


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𝜒bJ(nP)

⟨𝓞 ⟩ 𝜒bJ(nP)(3S1[8])

⟨𝓞 ⟩ (3P0[1]) 𝜒bJ(nP)

Chromoelectric field

EFT AND LHC PHYSICS

PRODUCTION OF AT LHC▸ We compared our predictions of 𝜒bJ(nP)

production rates at the LHC (normalized to 𝚼 production rates) with measurements from the LHCb collaboration. 

▸ Our predictions depend on a single universal nonperturbative parameter that we determined from 𝜒cJ(1P) decay rates.

▸ This is the first prediction of heavy quarkonium production rates that does not rely on previous measurements of production rates.


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𝜒bJ(nP)

LHCb, Eur.Phys.J. C74 (2014) no.10, 3092

EFT AND LHC PHYSICS

SUMMARY▸ Effective field theories lets us separate the high-energy perturbative

physics from the challenging low-energy nonperturbative physics in QCD.

▸ We used nonrelativistic QCD effective field theory to study production rates of heavy quarkonia, which are the simplest nonperturbative systems.

▸ By using the potential NRQCD formalism, we found that the nonperturbative part of 𝜒bJ(nP) production rates are determined from a single universal nonperturbative parameter in QCD. In principle, this parameter can be determined from first principles.

▸ We made the first prediction of 𝜒bJ(nP) production rates at the LHC that does not rely on previous measurements of the production rates.


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BACKUP

EFT AND LHC PHYSICS

GRAVITATIONAL EXAMPLE▸ Earth’s gravitational potential for r ≫ R⊕ is given by   

▸ The first term falls off like 1/r, and is accurate if the earth is a homogeneous sphere. The coefficient is just the earth mass.

▸ The second term falls off like 1/r3, and becomes important at distances closer to earth or if we need high accuracy.  The coefficient depends only on the mass distribution of earth.

▸ The higher order terms like 1/r4, 1/r5… of decreasing importance can be truncated to desired accuracy in (R⊕/r)n.


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(J2≈0.001)

Simplified case assuming cylindrical symmetry, taken from Am. J. Phys. 82, 769 (2014)

θ

r

EFT AND LHC PHYSICS

GRAVITATIONAL EXAMPLE▸ Earth’s gravitational potential for r ≫ R⊕   

▸ The coefficients of 1/rn depend only on the internal structure of the earth, at distances smaller than R⊕.

▸ Therefore, the formula describes how the internal structure of earth at distance scales smaller than R⊕ affects the gravity around earth farther than R⊕.

▸ The formula is universal : the same formula applies to other gravitational bodies, with different coefficients.


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r

Simplified case assuming cylindrical symmetry, taken from Am. J. Phys. 82, 769 (2014)

EFT AND LHC PHYSICS

PRODUCTION OF AT LHC▸ We also compared our

predictions of 𝜒b2(1P) and 𝜒b1(1P) relative production rates at the LHC with measurements from the LHCb and CMS collaborations.

▸ Our predictions depend on a single universal nonperturbative parameter that we determined from 𝜒cJ(1P) decay rates.

▸ This is the first prediction of heavy quarkonium production rates that does not rely on previously measured production rates.


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𝜒bJ(nP)

LHCb, JHEP 10 (2013) 115 LHCb, JHEP 10 (2014) 088

CMS, Phys. Lett. B 743 (2015) 383

bridging high and low scale physics in effective field … · 2019. 12. 4. · eft and lhc physics...

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